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11.7: Quadratic Equations and Applications- Answers to the Homework Exercises

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    45116
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    Square Root Property

    1. \(7,-1\)
    1. \(9, 5\)
    1. \(4, -14\)
    1. \(-9\pm\sqrt{37}\)
    1. \(2\pm\sqrt{70}\)
    1. \(-4\pm 3\sqrt{7}\)
    1. \(\dfrac{2}{9},-\dfrac{4}{9}\)
    1. \(\dfrac{11}{3},\dfrac{1}{3}\)
    1. \(-6\pm 5\sqrt{3}\)
    1. \(-\dfrac{1}{2}\)
    1. \(4,-10\)
    1. \(\pm 2\sqrt{2}\)
    1. \(-9\pm 2\sqrt{7}\)
    1. \(-8\pm 3\sqrt{5}\)
    1. \(0,-3\)
    1. \(-\dfrac{2}{7},-\dfrac{10}{7}\)
    1. \(\dfrac{7}{4},\dfrac{3}{4}\)

    Completing the Square

    1. \(225\); \((x-15)^2\)
    1. \(\dfrac{225}{4}\); \(\left(x-\dfrac{15}{2}\right)^2\)
    1. \(144\); \((a-12)^2\)
    1. \(\dfrac{1}{324}\); \(\left(r-\dfrac{1}{18}\right)^2\)
    1. \(11,5\)
    1. \(-1\pm i\sqrt{\dfrac{19}{2}}\)
    1. \(-5+\sqrt{86}, -5-\sqrt{86}\)
    1. \(-1\pm i\sqrt{21}\)
    1. \(-5\pm 2i\)
    1. \(1\pm i\sqrt{2}\)
    1. \(4\pm i\sqrt{39}\)
    1. \(-1\pm i\sqrt{\dfrac{43}{6}}\)
    1. \(-\dfrac{5}{2}\pm\dfrac{i\sqrt{87}}{2}\)
    1. \(\dfrac{7}{2}\pm\dfrac{i\sqrt{139}}{2}\)
    1. \(\dfrac{9+\sqrt{21}}{2},\dfrac{9-\sqrt{21}}{2}\)
    1. \(1,-\dfrac{5}{2}\)
    1. \(4+2\sqrt{7},4-2\sqrt{7}\)
    1. \(1\pm 2i\sqrt{\dfrac{11}{3}}\)
    1. \(8+2\sqrt{29}, 8-2\sqrt{29}\)
    1. \(1,-3\)
    1. \(7+\sqrt{85},7-\sqrt{85}\)
    1. \(x=1\pm 1\sqrt{\dfrac{21}{5}}\)
    1. \(-1,-7\)
    1. \(-2-i\sqrt{\dfrac{37}{3}}\)
    1. \(\dfrac{-7+\sqrt{181}}{2},\dfrac{-7-\sqrt{181}}{2}\)
    1. \(\dfrac{5}{2}\pm 3i\sqrt{7}\)
    1. \(\dfrac{1}{2}\pm i\sqrt{163}\)
    1. \(8,7\)

    Quadratic Formula

    1. \(\dfrac{\sqrt{6}}{2},-\dfrac{\sqrt{6}}{2}\)
    1. \(\dfrac{\sqrt{6}}{2},-\dfrac{\sqrt{6}}{2}\)
    1. \(3,-3\)
    1. \(\dfrac{-3\pm i\sqrt{55}}{4}\)
    1. \(\dfrac{-3+\sqrt{401}}{14},\dfrac{-3-\sqrt{401}}{14}\)
    1. \(\dfrac{-1\pm i\sqrt{3}}{2}\)
    1. \(\dfrac{7+3\sqrt{21}}{10},\dfrac{7-3\sqrt{21}}{10}\)
    1. \(-1,-\dfrac{3}{2}\)
    1. \(4,-9\)
    1. \(\dfrac{-3+\sqrt{345}}{14},\dfrac{-3-\sqrt{345}}{14}\)
    1. \(\pm\dfrac{i\sqrt{6}}{3}\)
    1. \(\dfrac{-1\pm i\sqrt{29}}{5}\)
    1. \(\pm\dfrac{i\sqrt{2}}{2}\)
    1. \(\dfrac{3\pm i\sqrt{159}}{12}\)
    1. \(\dfrac{-5+\sqrt{137}}{8},\dfrac{-5-\sqrt{137}}{8}\)
    1. \(3,-\dfrac{1}{3}\)
    1. \(\dfrac{-5+\sqrt{337}}{12},\dfrac{-5-\sqrt{337}}{12}\)
    1. \(2\sqrt{2},-2\sqrt{2}\)
    1. \(\dfrac{3\pm 3i\sqrt{5}}{7}\)
    1. \(\dfrac{\sqrt{6}}{2},-\dfrac{\sqrt{6}}{2}\)

    Graph Quadratic Functions

    1. clipboard_e3c2d0091b454c104a36fb2864601180f.png
      Figure 11.7.1
    1. clipboard_ef777bc4489c72f477300d11516bb99c0.png
      Figure 11.7.2
    1. clipboard_e15e26af53e837a0ea0c39090cb99fec6.png
      Figure 11.7.3
    1. clipboard_ef8fce125d4e416a83fd860b6e755c996.png
      Figure 11.7.4
    1. clipboard_ec5187c055aec40958b218b1e327d1348.png
      Figure 11.7.5
    1. clipboard_ee442b96e37414f705b0c1aac7b50f315.png
      Figure 11.7.6
    1. clipboard_e2155797705f3d7d845bab7cf1eb425ec.png
      Figure 11.7.7
    1. clipboard_e75d74f174ece55deb5e9ed72d659da8d.png
      Figure 11.7.8
    1. clipboard_e70a35b8e0f09014b7e380c36e51ea99e.png
      Figure 11.7.9
    1. clipboard_e4131ef3f97fb5fa6f1934b4cd61308ae.png
      Figure 11.7.10
    1. \(f(x)=3(x-1)^2\)
    1. \(f(x)=\dfrac{1}{3}x^2\)
    1. \(f(x)=4(x+4)^2\)
    1. \(f(x)=3x^2-4\)
    1. clipboard_ebb34a63aab3c87d3fd8f5ef4e7beae52.png
      Figure 11.7.11
    1. clipboard_e85eceb8974428bfcf0f2931e617dfcbd.png
      Figure 11.7.12
    1. clipboard_ef0d61b8e9541e8c755651df5d5bb05f3.png
      Figure 11.7.13
    1. clipboard_e8a753b3414427b7a120d47dbd2f7725e.png
      Figure 11.7.14
    1. clipboard_e35adafa0e55aa4aa7c9b7b7844b1801c.png
      Figure 11.7.15

    Quadratic Inequalities

    1. \((-\infty, 3)\cup (6,\infty )\)
    2. \([-4,6]\)
    3. \((-1,3)\)
    4. \((-\infty, -6]\cup [-4,\infty )\)
    5. \((-\infty ,2)\cup (2,\infty )\)
    6. \((-\infty, -4]\cup [2,\infty )\)
    7. \([1,3]\)
    8. \(\left[-4,\dfrac{5}{3}\right]\)
    9. \((-\infty ,-4]\cup\left(\dfrac{5}{4},\infty\right)\)
    10. \(\left(-1,\dfrac{1}{3}\right)\)
    11. \(\left[0,\dfrac{7}{4}\right]\)
    12. \((-\infty, -6]\cup [0,\infty )\)
    13. No Solution
    14. All real numbers

    Applications with Quadratic Functions

    1. \(\left(\dfrac{5}{4},-\dfrac{57}{8}\right)\); \(-\dfrac{57}{8}\)
    2. \(\left(\dfrac{1}{2},-\dfrac{11}{2}\right)\); \(-\dfrac{11}{2}\)
    3. \((-1,1)\); \(1\)
    4. \(27.65\); \(3,896.99\)
    5. \(19.39\); \(2,236.84\)
    6. \(22.76\); \(2,666.19\)
    7. \(25\); \(8.88\)
    8. \(45\); \(14.88\)
    9. \(11\); \(551.25\) or \(550\)
    10. \(16\); \(480.5\) or \(480\)
    11. \(10\); \(361\) or \(360\)

    This page titled 11.7: Quadratic Equations and Applications- Answers to the Homework Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.