{"id":121,"date":"2026-01-12T15:49:12","date_gmt":"2026-01-12T15:49:12","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=121"},"modified":"2026-01-12T15:49:12","modified_gmt":"2026-01-12T15:49:12","slug":"quadratic-functions-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/quadratic-functions-get-stronger-answer-key\/","title":{"raw":"Quadratic Functions: Get Stronger Answer Key","rendered":"Quadratic Functions: Get Stronger Answer Key"},"content":{"raw":"

Introduction to Quadratic Functions and Parabolas<\/span><\/h2>\r\n
    \r\n \t
  1. [latex]g(x)=(x 1)^2\u22124,[\/latex]; Vertex: [latex](\u22121,\u22124)[\/latex]<\/li>\r\n \t
  2. [latex]f(x)=(x \\frac{5}{2})^2\u2212\\frac{33}{4}[\/latex]; Vertex: [latex](\u2212\\frac{5}{2},\u2212\\frac{33}{4})[\/latex]<\/li>\r\n \t
  3. [latex]f(x)=3(x\u22121)^2\u221212,[\/latex]; Vertex: [latex](1,\u221212)[\/latex]<\/li>\r\n \t
  4. [latex]f(x)=3(x\u2212\\frac{5}{6})^2\u2212\\frac{37}{12},[\/latex]; Vertex: [latex](\\frac{5}{6},\u2212\\frac{37}{12})[\/latex]<\/li>\r\n \t
  5. Minimum is [latex]\u2212\\frac{17}{2}[\/latex] and occurs at [latex]\\frac{5}{2}[\/latex]. Axis of symmetry is [latex]x=\\frac{5}{2}[\/latex].<\/li>\r\n \t
  6. Minimum is [latex]\u2212\\frac{17}{16}[\/latex] and occurs at [latex]\u2212\\frac{1}{8}[\/latex]. Axis of symmetry is [latex]x=\u2212\\frac{1}{8}[\/latex].<\/li>\r\n \t
  7. Minimum is [latex]\u2212\\frac{7}{2}[\/latex] and occurs at [latex]\u22123[\/latex]. Axis of symmetry is [latex]x=\u22123[\/latex].<\/li>\r\n \t
  8. Domain is [latex](\u2212\u221e,\u221e)[\/latex]. Range is [latex][2,\u221e)[\/latex].<\/li>\r\n \t
  9. Domain is [latex](\u2212\u221e,\u221e)[\/latex]. Range is [latex][\u22125,\u221e)[\/latex].<\/li>\r\n \t
  10. Domain is [latex](\u2212\u221e,\u221e)[\/latex]. Range is [latex][\u221212,\u221e)[\/latex].<\/li>\r\n \t
  11. [latex]f(x)=x^2+4x+3[\/latex]<\/li>\r\n \t
  12. [latex]f(x)=x^2\u22124x+7[\/latex]<\/li>\r\n \t
  13. [latex]f(x)=\u2212\\frac{1}{49}x^2 \\frac{6}{49}x \\frac{89}{49}[\/latex]<\/li>\r\n \t
  14. [latex]f(x)=x^2\u22122x+1[\/latex]<\/li>\r\n \t
  15. Vertex: [latex](3, \u221210)[\/latex], axis of symmetry: [latex]x = 3[\/latex], intercepts: [latex](3 +\\sqrt{10},0)[\/latex] and [latex](3-\\sqrt{10},0)[\/latex]<\/li>\r\n<\/ol>\r\n\r\n
      \r\n \t
    1. Vertex: [latex](\\frac{7}{2},\u2212\\frac{37}{4})[\/latex], axis of symmetry: [latex]x=\\frac{7}{2}[\/latex], [latex]y[\/latex]-intercept: [latex](0,3)[\/latex], [latex]x[\/latex]-intercepts: [latex](\\frac{7 \\sqrt{37}}{2},0),(\\frac{7-\\sqrt{37}}{2},0)[\/latex]<\/li>\r\n<\/ol>\r\n\"Graph\r\n
        \r\n \t
      1. Vertex: [latex](\\frac{3}{2},\u221212)[\/latex], axis of symmetry: [latex]x=\\frac{3}{2}[\/latex], intercept: [latex]( \\frac{3+2\\sqrt{3}}{2},0)[\/latex] and [latex]( \\frac{3-2\\sqrt{3}}{2},0)[\/latex]<\/li>\r\n \t
      2. [latex]f(x)=x^2+2x+3[\/latex]<\/li>\r\n \t
      3. [latex]f(x)=\u22123x^2\u22126x\u22121[\/latex]<\/li>\r\n \t
      4. [latex]f(x)=-\\frac{1}{4}x^2 -x+2[\/latex]<\/li>\r\n<\/ol>\r\n

        Complex Numbers and Operations<\/span><\/h2>\r\n
          \r\n \t
        1. \"A<\/li>\r\n \t
        2. \"A<\/li>\r\n \t
        3. \"A<\/li>\r\n \t
        4. \"A<\/li>\r\n \t
        5. \u00a0\"-2<\/li>\r\n \t
        6. \"4i<\/li>\r\n \t
        7. \"1+2i<\/li>\r\n \t
        8. \"-1-i<\/li>\r\n \t
        9. [latex]5-i[\/latex]<\/li>\r\n \t
        10. \u00a0[latex]5-4i[\/latex]<\/li>\r\n \t
        11. [latex]3-5i[\/latex]<\/li>\r\n \t
        12. [latex]-(6+i)[\/latex]<\/li>\r\n \t
        13. [latex]6+12i[\/latex]<\/li>\r\n \t
        14. [latex]10-2i[\/latex]<\/li>\r\n \t
        15. \u00a0[latex]14+2i[\/latex]<\/li>\r\n \t
        16. [latex]-2+6i[\/latex]<\/li>\r\n \t
        17. [latex]18+6i[\/latex]<\/li>\r\n \t
        18. [latex]7+3i[\/latex]<\/li>\r\n \t
        19. [latex](2+3i)(1-i) = 5+i.[\/latex]It appears that multiplying by [latex]1-i[\/latex] both scaled the number away from the origin, and rotated it clockwise about [latex]45\u00b0[\/latex].\r\n\"A<\/li>\r\n \t
        20. <\/li>\r\n<\/ol>\r\n

          Application of Quadratic Functions<\/span><\/h2>\r\n
            \r\n \t
          1. The revenue reaches the maximum value when [latex]1800[\/latex] thousand phones are produced.<\/li>\r\n \t
          2. [latex]2.449[\/latex] seconds<\/li>\r\n \t
          3. [latex]41[\/latex] trees per acre<\/li>\r\n<\/ol>","rendered":"

            Introduction to Quadratic Functions and Parabolas<\/span><\/h2>\n
              \n
            1. [latex]g(x)=(x 1)^2\u22124,[\/latex]; Vertex: [latex](\u22121,\u22124)[\/latex]<\/li>\n
            2. [latex]f(x)=(x \\frac{5}{2})^2\u2212\\frac{33}{4}[\/latex]; Vertex: [latex](\u2212\\frac{5}{2},\u2212\\frac{33}{4})[\/latex]<\/li>\n
            3. [latex]f(x)=3(x\u22121)^2\u221212,[\/latex]; Vertex: [latex](1,\u221212)[\/latex]<\/li>\n
            4. [latex]f(x)=3(x\u2212\\frac{5}{6})^2\u2212\\frac{37}{12},[\/latex]; Vertex: [latex](\\frac{5}{6},\u2212\\frac{37}{12})[\/latex]<\/li>\n
            5. Minimum is [latex]\u2212\\frac{17}{2}[\/latex] and occurs at [latex]\\frac{5}{2}[\/latex]. Axis of symmetry is [latex]x=\\frac{5}{2}[\/latex].<\/li>\n
            6. Minimum is [latex]\u2212\\frac{17}{16}[\/latex] and occurs at [latex]\u2212\\frac{1}{8}[\/latex]. Axis of symmetry is [latex]x=\u2212\\frac{1}{8}[\/latex].<\/li>\n
            7. Minimum is [latex]\u2212\\frac{7}{2}[\/latex] and occurs at [latex]\u22123[\/latex]. Axis of symmetry is [latex]x=\u22123[\/latex].<\/li>\n
            8. Domain is [latex](\u2212\u221e,\u221e)[\/latex]. Range is [latex][2,\u221e)[\/latex].<\/li>\n
            9. Domain is [latex](\u2212\u221e,\u221e)[\/latex]. Range is [latex][\u22125,\u221e)[\/latex].<\/li>\n
            10. Domain is [latex](\u2212\u221e,\u221e)[\/latex]. Range is [latex][\u221212,\u221e)[\/latex].<\/li>\n
            11. [latex]f(x)=x^2+4x+3[\/latex]<\/li>\n
            12. [latex]f(x)=x^2\u22124x+7[\/latex]<\/li>\n
            13. [latex]f(x)=\u2212\\frac{1}{49}x^2 \\frac{6}{49}x \\frac{89}{49}[\/latex]<\/li>\n
            14. [latex]f(x)=x^2\u22122x+1[\/latex]<\/li>\n
            15. Vertex: [latex](3, \u221210)[\/latex], axis of symmetry: [latex]x = 3[\/latex], intercepts: [latex](3 +\\sqrt{10},0)[\/latex] and [latex](3-\\sqrt{10},0)[\/latex]<\/li>\n<\/ol>\n

              \"image\"<\/p>\n

                \n
              1. Vertex: [latex](\\frac{7}{2},\u2212\\frac{37}{4})[\/latex], axis of symmetry: [latex]x=\\frac{7}{2}[\/latex], [latex]y[\/latex]-intercept: [latex](0,3)[\/latex], [latex]x[\/latex]-intercepts: [latex](\\frac{7 \\sqrt{37}}{2},0),(\\frac{7-\\sqrt{37}}{2},0)[\/latex]<\/li>\n<\/ol>\n

                \"Graph<\/p>\n

                  \n
                1. Vertex: [latex](\\frac{3}{2},\u221212)[\/latex], axis of symmetry: [latex]x=\\frac{3}{2}[\/latex], intercept: [latex]( \\frac{3+2\\sqrt{3}}{2},0)[\/latex] and [latex]( \\frac{3-2\\sqrt{3}}{2},0)[\/latex]\"image\"<\/li>\n
                2. [latex]f(x)=x^2+2x+3[\/latex]<\/li>\n
                3. [latex]f(x)=\u22123x^2\u22126x\u22121[\/latex]<\/li>\n
                4. [latex]f(x)=-\\frac{1}{4}x^2 -x+2[\/latex]<\/li>\n<\/ol>\n

                  Complex Numbers and Operations<\/span><\/h2>\n
                    \n
                  1. \"A<\/li>\n
                  2. \"A<\/li>\n
                  3. \"A<\/li>\n
                  4. \"A<\/li>\n
                  5. \u00a0\"-2<\/li>\n
                  6. \"4i<\/li>\n
                  7. \"1+2i<\/li>\n
                  8. \"-1-i<\/li>\n
                  9. [latex]5-i[\/latex]<\/li>\n
                  10. \u00a0[latex]5-4i[\/latex]<\/li>\n
                  11. [latex]3-5i[\/latex]<\/li>\n
                  12. [latex]-(6+i)[\/latex]<\/li>\n
                  13. [latex]6+12i[\/latex]<\/li>\n
                  14. [latex]10-2i[\/latex]<\/li>\n
                  15. \u00a0[latex]14+2i[\/latex]<\/li>\n
                  16. [latex]-2+6i[\/latex]<\/li>\n
                  17. [latex]18+6i[\/latex]<\/li>\n
                  18. [latex]7+3i[\/latex]<\/li>\n
                  19. [latex](2+3i)(1-i) = 5+i.[\/latex]It appears that multiplying by [latex]1-i[\/latex] both scaled the number away from the origin, and rotated it clockwise about [latex]45\u00b0[\/latex].
                    \n\"A<\/li>\n
                  20. <\/li>\n<\/ol>\n

                    Application of Quadratic Functions<\/span><\/h2>\n
                      \n
                    1. The revenue reaches the maximum value when [latex]1800[\/latex] thousand phones are produced.<\/li>\n
                    2. [latex]2.449[\/latex] seconds<\/li>\n
                    3. [latex]41[\/latex] trees per acre<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":106,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/121"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/121\/revisions"}],"predecessor-version":[{"id":129,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/121\/revisions\/129"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/106"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/121\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=121"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=121"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=121"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}