{"id":1998,"date":"2021-12-02T19:40:23","date_gmt":"2021-12-03T00:40:23","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-10-6\/"},"modified":"2022-11-02T10:38:59","modified_gmt":"2022-11-02T14:38:59","slug":"answer-key-10-6","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-10-6\/","title":{"raw":"Answer Key 10.6","rendered":"Answer Key 10.6"},"content":{"raw":"<ol>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl}\ny&amp;=&amp;0 \\\\\n0&amp;=&amp;x^2-2x-8 \\\\\n0&amp;=&amp;(x-4)(x+2) \\\\\nx&amp;=&amp;4,-2 \\\\ \\\\\n\\end{array}[\/latex]\n[latex]\\text{vertex: }\\begin{array}[t]{l}\n\\left[\\dfrac{-b}{2a}, f\\left(\\dfrac{-b}{2a}\\right)\\right] \\\\ \\\\\n(1,-9)\n\\end{array}[\/latex]\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll}\nx&amp;=&amp;\\dfrac{-b}{2a} \\\\ \\\\\nx&amp;=&amp; \\dfrac{-(-2)}{2(1)}\\Rightarrow \\dfrac{2}{2}\\text{ or }1 \\\\ \\\\\n\\therefore f(1)&amp;=&amp;1^2-2(1)-8 \\\\\n\\phantom{\\therefore}f(1)&amp;=&amp;-9\n\\end{array}[\/latex]\n<img class=\"alignnone wp-image-1986 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2021\/12\/answer-10.6_1-292x300.jpg\" alt=\"Graph with line of symetry through x axis at 1\" width=\"292\" height=\"300\"><\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl}\n0&amp;=&amp;x^2-2x-3 \\\\\n0&amp;=&amp;(x-3)(x+1) \\\\\nx&amp;=&amp;3,-1\n\\end{array}[\/latex]\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll}\nx&amp;=&amp; \\dfrac{-(-2)}{2(1)}\\Rightarrow \\dfrac{2}{2}\\text{ or }1\n\\end{array}[\/latex]\n[latex]\\text{vertex: }\\begin{array}[t]{rll}\nf(1)&amp;=&amp;1^2-2(1)-3 \\\\\nf(1)&amp;=&amp;1-2-3 \\\\\nf(1)&amp;=&amp;-4 \\\\ \\\\\n&amp;&amp;(1,-4)\n\\end{array}[\/latex]\n<img class=\"alignnone wp-image-1987 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_2-295x300.jpg\" alt=\"Graph with line of symmetry through (1,0)\" width=\"295\" height=\"300\"><\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl}\n0&amp;=&amp;2x^2-12x+10 \\\\\n0&amp;=&amp;2(x^2-6x+5) \\\\\n0&amp;=&amp;2(x-5)(x-1) \\\\\nx&amp;=&amp;5,1\n\\end{array}[\/latex]\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll}\nx&amp;=&amp;\\dfrac{-b}{2a} \\\\ \\\\\nx&amp;=&amp; \\dfrac{-6}{2(1)}\\Rightarrow \\dfrac{6}{2}\\text{ or }3\n\\end{array}[\/latex]\n[latex]\\text{vertex: }\\begin{array}[t]{rll}\nf(3)&amp;=&amp;2(3)^2-12(3)+10 \\\\\nf(3)&amp;=&amp;18-36+10 \\\\\nf(3)&amp;=&amp;-8 \\\\ \\\\\n&amp;&amp;(3,-8)\n\\end{array}[\/latex]\n<img class=\"alignnone wp-image-1988 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_3-262x300.jpg\" alt=\"Test of intercept with line of symmetry through x=3\" width=\"262\" height=\"300\"><\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl}\n0&amp;=&amp;2x^2-12x+16 \\\\\n0&amp;=&amp;2(x^2-6x+8) \\\\\n0&amp;=&amp;2(x-4)(x-2) \\\\\nx&amp;=&amp;4,2\n\\end{array}[\/latex]\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll}\nx&amp;=&amp;\\dfrac{-b}{2a} \\\\ \\\\\nx&amp;=&amp; \\dfrac{-(-12)}{2(2)}\\Rightarrow \\dfrac{12}{4}\\text{ or }3\n\\end{array}[\/latex]\n[latex]\\text{vertex: }\\begin{array}[t]{rll}\nf(3)&amp;=&amp;2(3)^2-12(3)+16 \\\\\nf(3)&amp;=&amp;18-36+16 \\\\\nf(3)&amp;=&amp;-2 \\\\ \\\\\n&amp;&amp;(3,-2)\n\\end{array}[\/latex]\n<img class=\"alignnone wp-image-1989 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_4-293x300.jpg\" alt=\"Line of symmetry through x=4\" width=\"293\" height=\"300\"><\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl}\n0&amp;=&amp;-2x^2+12x-18 \\\\\n0&amp;=&amp;-2(x^2-6x+9) \\\\\n0&amp;=&amp;-2(x-3)(x-3) \\\\\nx&amp;=&amp;3\n\\end{array}[\/latex]\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll}\nx&amp;=&amp;\\dfrac{-b}{2a} \\\\ \\\\\nx&amp;=&amp; \\dfrac{-12}{2(-2)}\\Rightarrow \\dfrac{-12}{-4}\\text{ or }3\n\\end{array}[\/latex]\n[latex]\\text{vertex: }\\begin{array}[t]{rll}\nf(3)&amp;=&amp;-2(3)^2-12(3)-18 \\\\\nf(3)&amp;=&amp;-18+36-18 \\\\\nf(3)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;(0,3)\n\\end{array}[\/latex]\n<img class=\"alignnone wp-image-1990 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_5-300x274.jpg\" alt=\"Line of symmetry through x=4\" width=\"300\" height=\"274\"><\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl}\n0&amp;=&amp;-2x^2+12x-10 \\\\\n0&amp;=&amp;-2(x^2-6x+5) \\\\\n0&amp;=&amp;-2(x-5)(x-1) \\\\\nx&amp;=&amp;5,1\n\\end{array}[\/latex]\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll}\nx&amp;=&amp;\\dfrac{-b}{2a} \\\\ \\\\\nx&amp;=&amp; \\dfrac{-12}{2(-2)}\\Rightarrow \\dfrac{-12}{-4}\\text{ or }3\n\\end{array}[\/latex]\n[latex]\\text{vertex: }\\begin{array}[t]{rll}\nf(3)&amp;=&amp;-2(3)^2-12(3)-10 \\\\\nf(3)&amp;=&amp;-18+36-10 \\\\\nf(3)&amp;=&amp;8 \\\\ \\\\\n&amp;&amp;(3,8)\n\\end{array}[\/latex]\n<img class=\"alignnone wp-image-1991 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_6-300x292.jpg\" alt=\"Intercept test with line of symmetry through x=3\" width=\"300\" height=\"292\"><\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl}\n0&amp;=&amp;-3x^2+24x-45 \\\\\n0&amp;=&amp;-3(x^2-8x+15) \\\\\n0&amp;=&amp;-3(x-3)(x-5) \\\\\nx&amp;=&amp;3,5\n\\end{array}[\/latex]\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll}\nx&amp;=&amp;\\dfrac{-b}{2a} \\\\ \\\\\nx&amp;=&amp; \\dfrac{-24}{2(-3)}\\Rightarrow \\dfrac{-24}{-6}\\text{ or }4\n\\end{array}[\/latex]\n[latex]\\text{vertex: }\\begin{array}[t]{rll}\nf(4)&amp;=&amp;-3(4)^2+24(4)-45 \\\\\nf(4)&amp;=&amp;-48+96-45 \\\\\nf(4)&amp;=&amp;3 \\\\ \\\\\n&amp;&amp;(4,3)\n\\end{array}[\/latex]\n<img class=\"alignnone wp-image-1992 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_7-300x288.jpg\" alt=\"Line of symmtery x=5\" width=\"300\" height=\"288\"><\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl}\n0&amp;=&amp;-2(x^2+2x)+6 \\\\\n0&amp;=&amp;-2x^2-4x+6 \\\\\n0&amp;=&amp;-2(x^2+2x-3) \\\\\n0&amp;=&amp;-2(x+3)(x-1) \\\\\nx&amp;=&amp;-3,1\n\\end{array}[\/latex]\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll}\nx&amp;=&amp;\\dfrac{-b}{2a} \\\\ \\\\\nx&amp;=&amp; \\dfrac{-(-4)}{2(-2)}\\Rightarrow \\dfrac{4}{-4}\\text{ or }-1\n\\end{array}[\/latex]\n[latex]\\text{vertex: }\\begin{array}[t]{rll}\nf(-1)&amp;=&amp;-2(-1)^2-4(-1)+6 \\\\\nf(-1)&amp;=&amp;-2+4+6 \\\\\nf(-1)&amp;=&amp;8 \\\\ \\\\\n&amp;&amp;(-1,8)\n\\end{array}[\/latex]\n<img class=\"alignnone wp-image-1993 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_8-292x300.jpg\" alt=\"Graph with line of symmetry x=-1\" width=\"292\" height=\"300\"><\/li>\n \t<li>[latex]\\text{line of symmetry: }x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-6)}{2(3)}\\Rightarrow \\dfrac{6}{6}\\text{ or }1[\/latex]\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<th style=\"width: 50%;\" scope=\"col\">[latex]x[\/latex]<\/th>\n<th style=\"width: 50%;\" scope=\"col\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3<\/td>\n<td style=\"width: 50%;\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">2<\/td>\n<td style=\"width: 50%;\">\u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">1<\/td>\n<td style=\"width: 50%;\">\u22129<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">0<\/td>\n<td style=\"width: 50%;\">\u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22121<\/td>\n<td style=\"width: 50%;\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<img class=\"alignnone wp-image-1994 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_9-262x300.jpg\" alt=\"Intercept test\" width=\"262\" height=\"300\"><\/li>\n \t<li>[latex]\\text{line of symmetry: }x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-4)}{2(2)}\\Rightarrow \\dfrac{4}{4}\\text{ or }1[\/latex]\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<th style=\"width: 50%;\" scope=\"col\">[latex]x[\/latex]<\/th>\n<th style=\"width: 50%;\" scope=\"col\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3<\/td>\n<td style=\"width: 50%;\">3<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">2<\/td>\n<td style=\"width: 50%;\">\u22123<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">1<\/td>\n<td style=\"width: 50%;\">\u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">0<\/td>\n<td style=\"width: 50%;\">\u22123<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22121<\/td>\n<td style=\"width: 50%;\">3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<img class=\"alignnone wp-image-1995 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_10-300x271.jpg\" alt=\"Line of symmetry x=1\" width=\"300\" height=\"271\"><\/li>\n \t<li>[latex]\\text{line of symmetry: }x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-4}{2(-1)}\\Rightarrow \\dfrac{-4}{-2}\\text{ or }2[\/latex]\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<th style=\"width: 50%;\" scope=\"col\">[latex]x[\/latex]<\/th>\n<th style=\"width: 50%;\" scope=\"col\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5<\/td>\n<td style=\"width: 50%;\">\u22123<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">4<\/td>\n<td style=\"width: 50%;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3<\/td>\n<td style=\"width: 50%;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">2<\/td>\n<td style=\"width: 50%;\">6<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">1<\/td>\n<td style=\"width: 50%;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">0<\/td>\n<td style=\"width: 50%;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22121<\/td>\n<td style=\"width: 50%;\">\u22123<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<img class=\"alignnone wp-image-1996 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_11-288x300.jpg\" alt=\"Line of symmetry x=2\" width=\"288\" height=\"300\"><\/li>\n \t<li>[latex]\\text{line of symmetry: }x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-6)}{2(-3)}\\Rightarrow \\dfrac{6}{-6}\\text{ or }-1[\/latex]\n<table style=\"border-collapse: collapse; width: 100%; height: 108px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 18px;\">\n<th style=\"width: 50%; height: 18px;\" scope=\"col\">[latex]x[\/latex]<\/th>\n<th style=\"width: 50%; height: 18px;\" scope=\"col\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 50%; height: 18px;\">1<\/td>\n<td style=\"width: 50%; height: 18px;\">\u22127<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 50%; height: 18px;\">0<\/td>\n<td style=\"width: 50%; height: 18px;\">2<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 50%; height: 18px;\">\u22121<\/td>\n<td style=\"width: 50%; height: 18px;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22122<\/td>\n<td style=\"width: 50%;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22123<\/td>\n<td style=\"width: 50%;\">\u22127<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<img class=\"alignnone wp-image-1997 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_12-293x300.jpg\" alt=\"Line of symmetry x=1\" width=\"293\" height=\"300\"><\/li>\n<\/ol>","rendered":"<ol>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl} y&=&0 \\\\ 0&=&x^2-2x-8 \\\\ 0&=&(x-4)(x+2) \\\\ x&=&4,-2 \\\\ \\\\ \\end{array}[\/latex]<br \/>\n[latex]\\text{vertex: }\\begin{array}[t]{l} \\left[\\dfrac{-b}{2a}, f\\left(\\dfrac{-b}{2a}\\right)\\right] \\\\ \\\\ (1,-9) \\end{array}[\/latex]<br \/>\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll} x&=&\\dfrac{-b}{2a} \\\\ \\\\ x&=& \\dfrac{-(-2)}{2(1)}\\Rightarrow \\dfrac{2}{2}\\text{ or }1 \\\\ \\\\ \\therefore f(1)&=&1^2-2(1)-8 \\\\ \\phantom{\\therefore}f(1)&=&-9 \\end{array}[\/latex]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1986 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2021\/12\/answer-10.6_1-292x300.jpg\" alt=\"Graph with line of symetry through x axis at 1\" width=\"292\" height=\"300\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2021\/12\/answer-10.6_1-292x300.jpg 292w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2021\/12\/answer-10.6_1-65x67.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2021\/12\/answer-10.6_1-225x232.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2021\/12\/answer-10.6_1.jpg 343w\" sizes=\"auto, (max-width: 292px) 100vw, 292px\" \/><\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl} 0&=&x^2-2x-3 \\\\ 0&=&(x-3)(x+1) \\\\ x&=&3,-1 \\end{array}[\/latex]<br \/>\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll} x&=& \\dfrac{-(-2)}{2(1)}\\Rightarrow \\dfrac{2}{2}\\text{ or }1 \\end{array}[\/latex]<br \/>\n[latex]\\text{vertex: }\\begin{array}[t]{rll} f(1)&=&1^2-2(1)-3 \\\\ f(1)&=&1-2-3 \\\\ f(1)&=&-4 \\\\ \\\\ &&(1,-4) \\end{array}[\/latex]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1987 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_2-295x300.jpg\" alt=\"Graph with line of symmetry through (1,0)\" width=\"295\" height=\"300\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_2-295x300.jpg 295w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_2-65x66.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_2-225x229.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_2.jpg 304w\" sizes=\"auto, (max-width: 295px) 100vw, 295px\" \/><\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl} 0&=&2x^2-12x+10 \\\\ 0&=&2(x^2-6x+5) \\\\ 0&=&2(x-5)(x-1) \\\\ x&=&5,1 \\end{array}[\/latex]<br \/>\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll} x&=&\\dfrac{-b}{2a} \\\\ \\\\ x&=& \\dfrac{-6}{2(1)}\\Rightarrow \\dfrac{6}{2}\\text{ or }3 \\end{array}[\/latex]<br \/>\n[latex]\\text{vertex: }\\begin{array}[t]{rll} f(3)&=&2(3)^2-12(3)+10 \\\\ f(3)&=&18-36+10 \\\\ f(3)&=&-8 \\\\ \\\\ &&(3,-8) \\end{array}[\/latex]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1988 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_3-262x300.jpg\" alt=\"Test of intercept with line of symmetry through x=3\" width=\"262\" height=\"300\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_3-262x300.jpg 262w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_3-65x74.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_3-225x257.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_3.jpg 320w\" sizes=\"auto, (max-width: 262px) 100vw, 262px\" \/><\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl} 0&=&2x^2-12x+16 \\\\ 0&=&2(x^2-6x+8) \\\\ 0&=&2(x-4)(x-2) \\\\ x&=&4,2 \\end{array}[\/latex]<br \/>\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll} x&=&\\dfrac{-b}{2a} \\\\ \\\\ x&=& \\dfrac{-(-12)}{2(2)}\\Rightarrow \\dfrac{12}{4}\\text{ or }3 \\end{array}[\/latex]<br \/>\n[latex]\\text{vertex: }\\begin{array}[t]{rll} f(3)&=&2(3)^2-12(3)+16 \\\\ f(3)&=&18-36+16 \\\\ f(3)&=&-2 \\\\ \\\\ &&(3,-2) \\end{array}[\/latex]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1989 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_4-293x300.jpg\" alt=\"Line of symmetry through x=4\" width=\"293\" height=\"300\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_4-293x300.jpg 293w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_4-65x67.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_4-225x231.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_4.jpg 322w\" sizes=\"auto, (max-width: 293px) 100vw, 293px\" \/><\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl} 0&=&-2x^2+12x-18 \\\\ 0&=&-2(x^2-6x+9) \\\\ 0&=&-2(x-3)(x-3) \\\\ x&=&3 \\end{array}[\/latex]<br \/>\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll} x&=&\\dfrac{-b}{2a} \\\\ \\\\ x&=& \\dfrac{-12}{2(-2)}\\Rightarrow \\dfrac{-12}{-4}\\text{ or }3 \\end{array}[\/latex]<br \/>\n[latex]\\text{vertex: }\\begin{array}[t]{rll} f(3)&=&-2(3)^2-12(3)-18 \\\\ f(3)&=&-18+36-18 \\\\ f(3)&=&0 \\\\ \\\\ &&(0,3) \\end{array}[\/latex]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1990 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_5-300x274.jpg\" alt=\"Line of symmetry through x=4\" width=\"300\" height=\"274\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_5-300x274.jpg 300w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_5-65x59.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_5-225x205.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_5.jpg 320w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl} 0&=&-2x^2+12x-10 \\\\ 0&=&-2(x^2-6x+5) \\\\ 0&=&-2(x-5)(x-1) \\\\ x&=&5,1 \\end{array}[\/latex]<br \/>\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll} x&=&\\dfrac{-b}{2a} \\\\ \\\\ x&=& \\dfrac{-12}{2(-2)}\\Rightarrow \\dfrac{-12}{-4}\\text{ or }3 \\end{array}[\/latex]<br \/>\n[latex]\\text{vertex: }\\begin{array}[t]{rll} f(3)&=&-2(3)^2-12(3)-10 \\\\ f(3)&=&-18+36-10 \\\\ f(3)&=&8 \\\\ \\\\ &&(3,8) \\end{array}[\/latex]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1991 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_6-300x292.jpg\" alt=\"Intercept test with line of symmetry through x=3\" width=\"300\" height=\"292\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_6-300x292.jpg 300w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_6-65x63.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_6-225x219.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_6.jpg 321w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl} 0&=&-3x^2+24x-45 \\\\ 0&=&-3(x^2-8x+15) \\\\ 0&=&-3(x-3)(x-5) \\\\ x&=&3,5 \\end{array}[\/latex]<br \/>\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll} x&=&\\dfrac{-b}{2a} \\\\ \\\\ x&=& \\dfrac{-24}{2(-3)}\\Rightarrow \\dfrac{-24}{-6}\\text{ or }4 \\end{array}[\/latex]<br \/>\n[latex]\\text{vertex: }\\begin{array}[t]{rll} f(4)&=&-3(4)^2+24(4)-45 \\\\ f(4)&=&-48+96-45 \\\\ f(4)&=&3 \\\\ \\\\ &&(4,3) \\end{array}[\/latex]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1992 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_7-300x288.jpg\" alt=\"Line of symmtery x=5\" width=\"300\" height=\"288\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_7-300x288.jpg 300w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_7-65x62.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_7-225x216.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_7.jpg 318w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\text{intercepts: }\\begin{array}[t]{rrl} 0&=&-2(x^2+2x)+6 \\\\ 0&=&-2x^2-4x+6 \\\\ 0&=&-2(x^2+2x-3) \\\\ 0&=&-2(x+3)(x-1) \\\\ x&=&-3,1 \\end{array}[\/latex]<br \/>\n[latex]\\text{line of symmetry: }\\begin{array}[t]{rll} x&=&\\dfrac{-b}{2a} \\\\ \\\\ x&=& \\dfrac{-(-4)}{2(-2)}\\Rightarrow \\dfrac{4}{-4}\\text{ or }-1 \\end{array}[\/latex]<br \/>\n[latex]\\text{vertex: }\\begin{array}[t]{rll} f(-1)&=&-2(-1)^2-4(-1)+6 \\\\ f(-1)&=&-2+4+6 \\\\ f(-1)&=&8 \\\\ \\\\ &&(-1,8) \\end{array}[\/latex]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1993 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_8-292x300.jpg\" alt=\"Graph with line of symmetry x=-1\" width=\"292\" height=\"300\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_8-292x300.jpg 292w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_8-65x67.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_8-225x231.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_8.jpg 328w\" sizes=\"auto, (max-width: 292px) 100vw, 292px\" \/><\/li>\n<li>[latex]\\text{line of symmetry: }x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-6)}{2(3)}\\Rightarrow \\dfrac{6}{6}\\text{ or }1[\/latex]<br \/>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<th style=\"width: 50%;\" scope=\"col\">[latex]x[\/latex]<\/th>\n<th style=\"width: 50%;\" scope=\"col\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3<\/td>\n<td style=\"width: 50%;\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">2<\/td>\n<td style=\"width: 50%;\">\u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">1<\/td>\n<td style=\"width: 50%;\">\u22129<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">0<\/td>\n<td style=\"width: 50%;\">\u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22121<\/td>\n<td style=\"width: 50%;\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1994 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_9-262x300.jpg\" alt=\"Intercept test\" width=\"262\" height=\"300\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_9-262x300.jpg 262w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_9-65x74.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_9-225x257.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_9.jpg 319w\" sizes=\"auto, (max-width: 262px) 100vw, 262px\" \/><\/li>\n<li>[latex]\\text{line of symmetry: }x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-4)}{2(2)}\\Rightarrow \\dfrac{4}{4}\\text{ or }1[\/latex]<br \/>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<th style=\"width: 50%;\" scope=\"col\">[latex]x[\/latex]<\/th>\n<th style=\"width: 50%;\" scope=\"col\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3<\/td>\n<td style=\"width: 50%;\">3<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">2<\/td>\n<td style=\"width: 50%;\">\u22123<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">1<\/td>\n<td style=\"width: 50%;\">\u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">0<\/td>\n<td style=\"width: 50%;\">\u22123<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22121<\/td>\n<td style=\"width: 50%;\">3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1995 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_10-300x271.jpg\" alt=\"Line of symmetry x=1\" width=\"300\" height=\"271\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_10-300x271.jpg 300w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_10-65x59.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_10-225x203.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_10.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li>[latex]\\text{line of symmetry: }x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-4}{2(-1)}\\Rightarrow \\dfrac{-4}{-2}\\text{ or }2[\/latex]<br \/>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<th style=\"width: 50%;\" scope=\"col\">[latex]x[\/latex]<\/th>\n<th style=\"width: 50%;\" scope=\"col\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5<\/td>\n<td style=\"width: 50%;\">\u22123<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">4<\/td>\n<td style=\"width: 50%;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3<\/td>\n<td style=\"width: 50%;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">2<\/td>\n<td style=\"width: 50%;\">6<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">1<\/td>\n<td style=\"width: 50%;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">0<\/td>\n<td style=\"width: 50%;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22121<\/td>\n<td style=\"width: 50%;\">\u22123<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1996 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_11-288x300.jpg\" alt=\"Line of symmetry x=2\" width=\"288\" height=\"300\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_11-288x300.jpg 288w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_11-65x68.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_11-225x235.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_11.jpg 306w\" sizes=\"auto, (max-width: 288px) 100vw, 288px\" \/><\/li>\n<li>[latex]\\text{line of symmetry: }x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-6)}{2(-3)}\\Rightarrow \\dfrac{6}{-6}\\text{ or }-1[\/latex]<br \/>\n<table style=\"border-collapse: collapse; width: 100%; height: 108px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<th style=\"width: 50%; height: 18px;\" scope=\"col\">[latex]x[\/latex]<\/th>\n<th style=\"width: 50%; height: 18px;\" scope=\"col\">[latex]y[\/latex]<\/th>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 50%; height: 18px;\">1<\/td>\n<td style=\"width: 50%; height: 18px;\">\u22127<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 50%; height: 18px;\">0<\/td>\n<td style=\"width: 50%; height: 18px;\">2<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 50%; height: 18px;\">\u22121<\/td>\n<td style=\"width: 50%; height: 18px;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22122<\/td>\n<td style=\"width: 50%;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u22123<\/td>\n<td style=\"width: 50%;\">\u22127<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1997 size-medium\" src=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_12-293x300.jpg\" alt=\"Line of symmetry x=1\" width=\"293\" height=\"300\" srcset=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_12-293x300.jpg 293w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_12-65x67.jpg 65w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_12-225x230.jpg 225w, https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-content\/uploads\/sites\/304\/2022\/11\/answer-10.6_12.jpg 334w\" sizes=\"auto, (max-width: 293px) 100vw, 293px\" \/><\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":98,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1998","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1998","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1998\/revisions"}],"predecessor-version":[{"id":1999,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1998\/revisions\/1999"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1998\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1998"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1998"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1998"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}