{"id":1784,"date":"2019-08-12T12:59:59","date_gmt":"2019-08-12T16:59:59","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1784"},"modified":"2019-12-29T19:55:41","modified_gmt":"2019-12-30T00:55:41","slug":"answer-key-10-6","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-10-6\/","title":{"raw":"Answer Key 10.6","rendered":"Answer Key 10.6"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\text{intercepts: }\\)\\(\\begin{array}{rrl}\r\ny&=&0 \\\\\r\n0&=&x^2-2x-8 \\\\\r\n0&=&(x-4)(x+2) \\\\\r\nx&=&4,-2 \\\\\r\n\\end{array}\\)\\(\\text{vertex: }\\)\\(\\begin{array}{l}\r\n\\left[\\dfrac{-b}{2a}, f\\left(\\dfrac{-b}{2a}\\right)\\right] \\\\ \\\\\r\n(1,-9)\r\n\\end{array}\\)\\(\\text{line of symmetry: }\\)\\(\\begin{array}{rll}\r\nx&=&\\dfrac{-b}{2a} \\\\ \\\\\r\nx&=& \\dfrac{-(-2)}{2(1)}\\Rightarrow \\dfrac{2}{2}\\text{ or }1 \\\\ \\\\\r\n\\therefore f(1)&=&1^2-2(1)-8 \\\\\r\n\\phantom{\\therefore}f(1)&=&-9\r\n\\end{array}\\)\r\n\"Graph<\/li>\r\n \t
  2. \\(\\text{intercepts: }\\)\\(\\begin{array}{rrl}\r\n0&=&x^2-2x-3 \\\\\r\n0&=&(x-3)(x+1) \\\\\r\nx&=&3,-1\r\n\\end{array}\\)\\(\\text{line of symmetry: }\\)\\(\\begin{array}{rll}\r\nx&=& \\dfrac{-(-2)}{2(1)}\\Rightarrow \\dfrac{2}{2}\\text{ or }1\r\n\\end{array}\\)\\(\\text{vertex: }\\)\\(\\begin{array}{rll}\r\nf(1)&=&1^2-2(1)-3 \\\\\r\nf(1)&=&1-2-3 \\\\\r\nf(1)&=&-4 \\\\ \\\\\r\n&&(1,-4)\r\n\\end{array}\\)\r\n\"Graph<\/li>\r\n \t
  3. \\(\\text{intercepts: }\\)\\(\\begin{array}{rrl}\r\n0&=&2x^2-12x+10 \\\\\r\n0&=&2(x^2-6x+5) \\\\\r\n0&=&2(x-5)(x-1) \\\\\r\nx&=&5,1\r\n\\end{array}\\)\\(\\text{line of symmetry: }\\)\\(\\begin{array}{rll}\r\nx&=&\\dfrac{-b}{2a} \\\\ \\\\\r\nx&=& \\dfrac{-6}{2(1)}\\Rightarrow \\dfrac{6}{2}\\text{ or }3\r\n\\end{array}\\)\\(\\text{vertex: }\\)\\(\\begin{array}{rll}\r\nf(3)&=&2(3)^2-12(3)+10 \\\\\r\nf(3)&=&18-36+10 \\\\\r\nf(3)&=&-8 \\\\ \\\\\r\n&&(3,-8)\r\n\\end{array}\\)\r\n\"Test<\/li>\r\n \t
  4. \\(\\text{intercepts: }\\)\\(\\begin{array}{rrl}\r\n0&=&2x^2-12x+16 \\\\\r\n0&=&2(x^2-6x+8) \\\\\r\n0&=&2(x-4)(x-2) \\\\\r\nx&=&4,2\r\n\\end{array}\\)\\(\\text{line of symmetry: }\\)\\(\\begin{array}{rll}\r\nx&=&\\dfrac{-b}{2a} \\\\ \\\\\r\nx&=& \\dfrac{-(-12)}{2(2)}\\Rightarrow \\dfrac{12}{4}\\text{ or }3\r\n\\end{array}\\)\\(\\text{vertex: }\\)\\(\\begin{array}{rll}\r\nf(3)&=&2(3)^2-12(3)+16 \\\\\r\nf(3)&=&18-36+16 \\\\\r\nf(3)&=&-2 \\\\ \\\\\r\n&&(3,-2)\r\n\\end{array}\\)\r\n\"Line<\/li>\r\n \t
  5. \\(\\text{intercepts: }\\)\\(\\begin{array}{rrl}\r\n0&=&-2x^2+12x-18 \\\\\r\n0&=&-2(x^2-6x+9) \\\\\r\n0&=&-2(x-3)(x-3) \\\\\r\nx&=&3\r\n\\end{array}\\)\\(\\text{line of symmetry: }\\)\\(\\begin{array}{rll}\r\nx&=&\\dfrac{-b}{2a} \\\\ \\\\\r\nx&=& \\dfrac{-12}{2(-2)}\\Rightarrow \\dfrac{-12}{-4}\\text{ or }3\r\n\\end{array}\\)\\(\\text{vertex: }\\)\\(\\begin{array}{rll}\r\nf(3)&=&-2(3)^2-12(3)-18 \\\\\r\nf(3)&=&-18+36-18 \\\\\r\nf(3)&=&0 \\\\ \\\\\r\n&&(0,3)\r\n\\end{array}\\)\r\n\"Line<\/li>\r\n \t
  6. \\(\\text{intercepts: }\\)\\(\\begin{array}{rrl}\r\n0&=&-2x^2+12x-10 \\\\\r\n0&=&-2(x^2-6x+5) \\\\\r\n0&=&-2(x-5)(x-1) \\\\\r\nx&=&5,1\r\n\\end{array}\\)\\(\\text{line of symmetry: }\\)\\(\\begin{array}{rll}\r\nx&=&\\dfrac{-b}{2a} \\\\ \\\\\r\nx&=& \\dfrac{-12}{2(-2)}\\Rightarrow \\dfrac{-12}{-4}\\text{ or }3\r\n\\end{array}\\)\\(\\text{vertex: }\\)\\(\\begin{array}{rll}\r\nf(3)&=&-2(3)^2-12(3)-10 \\\\\r\nf(3)&=&-18+36-10 \\\\\r\nf(3)&=&8 \\\\ \\\\\r\n&&(3,8)\r\n\\end{array}\\)\r\n\"Intercept<\/li>\r\n \t
  7. \\(\\text{intercepts: }\\)\\(\\begin{array}{rrl}\r\n0&=&-3x^2+24x-45 \\\\\r\n0&=&-3(x^2-8x+15) \\\\\r\n0&=&-3(x-3)(x-5) \\\\\r\nx&=&3,5\r\n\\end{array}\\)\\(\\text{line of symmetry: }\\)\\(\\begin{array}{rll}\r\nx&=&\\dfrac{-b}{2a} \\\\ \\\\\r\nx&=& \\dfrac{-24}{2(-3)}\\Rightarrow \\dfrac{-24}{-6}\\text{ or }4\r\n\\end{array}\\)\\(\\text{vertex: }\\)\\(\\begin{array}{rll}\r\nf(4)&=&-3(4)^2+24(4)-45 \\\\\r\nf(4)&=&-48+96-45 \\\\\r\nf(4)&=&3 \\\\ \\\\\r\n&&(4,3)\r\n\\end{array}\\)\r\n\"Line<\/li>\r\n \t
  8. \\(\\text{intercepts: }\\)\\(\\begin{array}{rrl}\r\n0&=&-2(x^2+2x)+6 \\\\\r\n0&=&-2x^2-4x+6 \\\\\r\n0&=&-2(x^2+2x-3) \\\\\r\n0&=&-2(x+3)(x-1) \\\\\r\nx&=&-3,1\r\n\\end{array}\\)\\(\\text{line of symmetry: }\\)\\(\\begin{array}{rll}\r\nx&=&\\dfrac{-b}{2a} \\\\ \\\\\r\nx&=& \\dfrac{-(-4)}{2(-2)}\\Rightarrow \\dfrac{4}{-4}\\text{ or }-1\r\n\\end{array}\\)\\(\\text{vertex: }\\)\\(\\begin{array}{rll}\r\nf(-1)&=&-2(-1)^2-4(-1)+6 \\\\\r\nf(-1)&=&-2+4+6 \\\\\r\nf(-1)&=&8 \\\\ \\\\\r\n&&(-1,8)\r\n\\end{array}\\)\r\n\"Graph<\/li>\r\n \t
  9. \\(\\text{line of symmetry: } \\\\ \\)\r\n\\(x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-6)}{2(3)}\\Rightarrow \\dfrac{6}{6}\\text{ or }1\\)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    3<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n\u22125<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n\u22129<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n\u22125<\/td>\r\n<\/tr>\r\n
    \u22121<\/td>\r\n4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Intercept<\/li>\r\n \t
  10. \\(\\text{line of symmetry: } \\\\ \\)\r\n\\(x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-4)}{2(2)}\\Rightarrow \\dfrac{4}{4}\\text{ or }1\\)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    3<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n\u22123<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n\u22125<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n\u22123<\/td>\r\n<\/tr>\r\n
    \u22121<\/td>\r\n3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Line<\/li>\r\n \t
  11. \\(\\text{line of symmetry: } \\\\ \\)\r\n\\(x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-4}{2(-1)}\\Rightarrow \\dfrac{-4}{-2}\\text{ or }2\\)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    5<\/td>\r\n\u22123<\/td>\r\n<\/tr>\r\n
    4<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    3<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n6<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    \u22121<\/td>\r\n\u22123<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Line<\/li>\r\n \t
  12. \\(\\text{line of symmetry: } \\\\ \\)\r\n\\(x=\\dfrac{-b}{2a}\\Rightarrow \\dfrac{-(-6)}{2(-3)}\\Rightarrow \\dfrac{6}{-6}\\text{ or }-1\\)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    1<\/td>\r\n\u22127<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    \u22121<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    \u22123<\/td>\r\n\u22127<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Line<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\text{intercepts: }\"\"\begin{array}{rrl}\"\text{vertex: }\"\"\begin{array}{l}\"\text{line of symmetry: }\"\"\begin{array}{rll}
      \n\"Graph<\/li>\n
    2. \"\text{intercepts: }\"\"\begin{array}{rrl}\"\text{line of symmetry: }\"\"\begin{array}{rll}\"\text{vertex: }\"\"\begin{array}{rll}
      \n\"Graph<\/li>\n
    3. \"\text{intercepts: }\"\"\begin{array}{rrl}\"\text{line of symmetry: }\"\"\begin{array}{rll}\"\text{vertex: }\"\"\begin{array}{rll}
      \n\"Test<\/li>\n
    4. \"\text{intercepts: }\"\"\begin{array}{rrl}\"\text{line of symmetry: }\"\"\begin{array}{rll}\"\text{vertex: }\"\"\begin{array}{rll}
      \n\"Line<\/li>\n
    5. \"\text{intercepts: }\"\"\begin{array}{rrl}\"\text{line of symmetry: }\"\"\begin{array}{rll}\"\text{vertex: }\"\"\begin{array}{rll}
      \n\"Line<\/li>\n
    6. \"\text{intercepts: }\"\"\begin{array}{rrl}\"\text{line of symmetry: }\"\"\begin{array}{rll}\"\text{vertex: }\"\"\begin{array}{rll}
      \n\"Intercept<\/li>\n
    7. \"\text{intercepts: }\"\"\begin{array}{rrl}\"\text{line of symmetry: }\"\"\begin{array}{rll}\"\text{vertex: }\"\"\begin{array}{rll}
      \n\"Line<\/li>\n
    8. \"\text{intercepts: }\"\"\begin{array}{rrl}\"\text{line of symmetry: }\"\"\begin{array}{rll}\"\text{vertex: }\"\"\begin{array}{rll}
      \n\"Graph<\/li>\n
    9. \"\text{line of symmetry: } \\\"
      \n\"x=\dfrac{-b}{2a}\Rightarrow \dfrac{-(-6)}{2(3)}\Rightarrow \dfrac{6}{6}\text{ or }1\"<\/p>\n\n\n\n\n\n\n\n\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      3<\/td>\n4<\/td>\n<\/tr>\n
      2<\/td>\n\u22125<\/td>\n<\/tr>\n
      1<\/td>\n\u22129<\/td>\n<\/tr>\n
      0<\/td>\n\u22125<\/td>\n<\/tr>\n
      \u22121<\/td>\n4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Intercept<\/li>\n

    10. \"\text{line of symmetry: } \\\"
      \n\"x=\dfrac{-b}{2a}\Rightarrow \dfrac{-(-4)}{2(2)}\Rightarrow \dfrac{4}{4}\text{ or }1\"<\/p>\n\n\n\n\n\n\n\n\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      3<\/td>\n3<\/td>\n<\/tr>\n
      2<\/td>\n\u22123<\/td>\n<\/tr>\n
      1<\/td>\n\u22125<\/td>\n<\/tr>\n
      0<\/td>\n\u22123<\/td>\n<\/tr>\n
      \u22121<\/td>\n3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Line<\/li>\n

    11. \"\text{line of symmetry: } \\\"
      \n\"x=\dfrac{-b}{2a}\Rightarrow \dfrac{-4}{2(-1)}\Rightarrow \dfrac{-4}{-2}\text{ or }2\"<\/p>\n\n\n\n\n\n\n\n\n\n\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      5<\/td>\n\u22123<\/td>\n<\/tr>\n
      4<\/td>\n2<\/td>\n<\/tr>\n
      3<\/td>\n5<\/td>\n<\/tr>\n
      2<\/td>\n6<\/td>\n<\/tr>\n
      1<\/td>\n5<\/td>\n<\/tr>\n
      0<\/td>\n2<\/td>\n<\/tr>\n
      \u22121<\/td>\n\u22123<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Line<\/li>\n

    12. \"\text{line of symmetry: } \\\"
      \n\"x=\dfrac{-b}{2a}\Rightarrow \dfrac{-(-6)}{2(-3)}\Rightarrow \dfrac{6}{-6}\text{ or }-1\"<\/p>\n\n\n\n\n\n\n\n\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      1<\/td>\n\u22127<\/td>\n<\/tr>\n
      0<\/td>\n2<\/td>\n<\/tr>\n
      \u22121<\/td>\n5<\/td>\n<\/tr>\n
      \u22122<\/td>\n2<\/td>\n<\/tr>\n
      \u22123<\/td>\n\u22127<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Line<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":93,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1784","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1784","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":7,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1784\/revisions"}],"predecessor-version":[{"id":3748,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1784\/revisions\/3748"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1784\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1784"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1784"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1784"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}