We've updated our

TEXT

# Solutions

## Solutions to Try Its

1. The path passes through the origin and has vertex at $\left(-4,\text{ }7\right)$, so $\left(h\right)x=-\frac{7}{16}{\left(x+4\right)}^{2}+7$. To make the shot, $h\left(-7.5\right)$ would need to be about 4 but $h\left(-7.5\right)\approx 1.64$; he doesn’t make it. 2. $g\left(x\right)={x}^{2}-6x+13$ in general form; $g\left(x\right)={\left(x - 3\right)}^{2}+4$ in standard form 3. The domain is all real numbers. The range is $f\left(x\right)\ge \frac{8}{11}$, or $\left[\frac{8}{11},\infty \right)$. 4. y-intercept at (0, 13), No x-intercepts 5. a. 3 seconds  b. 256 feet  c. 7 seconds

## Solutions to Odd-Numbered Exercises

1. When written in that form, the vertex can be easily identified. 3. If $a=0$ then the function becomes a linear function. 5. If possible, we can use factoring. Otherwise, we can use the quadratic formula. 7. $f\left(x\right)={\left(x+1\right)}^{2}-2$, Vertex $\left(-1,-4\right)$ 9. $f\left(x\right)={\left(x+\frac{5}{2}\right)}^{2}-\frac{33}{4}$, Vertex $\left(-\frac{5}{2},-\frac{33}{4}\right)$ 11. $f\left(x\right)=3{\left(x - 1\right)}^{2}-12$, Vertex $\left(1,-12\right)$ 13. $f\left(x\right)=3{\left(x-\frac{5}{6}\right)}^{2}-\frac{37}{12}$, Vertex $\left(\frac{5}{6},-\frac{37}{12}\right)$ 15. Minimum is $-\frac{17}{2}$ and occurs at $\frac{5}{2}$. Axis of symmetry is $x=\frac{5}{2}$. 17. Minimum is $-\frac{17}{16}$ and occurs at $-\frac{1}{8}$. Axis of symmetry is $x=-\frac{1}{8}$. 19. Minimum is $-\frac{7}{2}$ and occurs at –3. Axis of symmetry is $x=-3$. 21. Domain is $\left(-\infty ,\infty \right)$. Range is $\left[2,\infty \right)$. 23. Domain is $\left(-\infty ,\infty \right)$. Range is $\left[-5,\infty \right)$. 25. Domain is $\left(-\infty ,\infty \right)$. Range is $\left[-12,\infty \right)$. 27. $\left\{2i\sqrt{2},-2i\sqrt{2}\right\}$ 29. $\left\{3i\sqrt{3},-3i\sqrt{3}\right\}$ 31. $\left\{2+i,2-i\right\}$ 33. $\left\{2+3i,2 - 3i\right\}$ 35. $\left\{5+i,5-i\right\}$ 37. $\left\{2+2\sqrt{6}, 2 - 2\sqrt{6}\right\}$ 39. $\left\{-\frac{1}{2}+\frac{3}{2}i, -\frac{1}{2}-\frac{3}{2}i\right\}$ 41. $\left\{-\frac{3}{5}+\frac{1}{5}i, -\frac{3}{5}-\frac{1}{5}i\right\}$ 43. $\left\{-\frac{1}{2}+\frac{1}{2}i\sqrt{7}, -\frac{1}{2}-\frac{1}{2}i\sqrt{7}\right\}$ 45. $f\left(x\right)={x}^{2}-4x+4$ 47. $f\left(x\right)={x}^{2}+1$ 49. $f\left(x\right)=\frac{6}{49}{x}^{2}+\frac{60}{49}x+\frac{297}{49}$ 51. $f\left(x\right)=-{x}^{2}+1$ 53. Vertex $\left(1,\text{ }-1\right)$, Axis of symmetry is $x=1$. Intercepts are $\left(0,0\right), \left(2,0\right)$. 55. Vertex $\left(\frac{5}{2},\frac{-49}{4}\right)$, Axis of symmetry is $\left(0,-6\right),\left(-1,0\right),\left(6,0\right)$. 57. Vertex $\left(\frac{5}{4}, -\frac{39}{8}\right)$, Axis of symmetry is $x=\frac{5}{4}$. Intercepts are $\left(0, -8\right)$. 59. $f\left(x\right)={x}^{2}-4x+1$ 61. $f\left(x\right)=-2{x}^{2}+8x - 1$ 63. $f\left(x\right)=\frac{1}{2}{x}^{2}-3x+\frac{7}{2}$ 65. $f\left(x\right)={x}^{2}+1$ 67. $f\left(x\right)=2-{x}^{2}$ 69. $f\left(x\right)=2{x}^{2}$ 71. The graph is shifted up or down (a vertical shift). 73. 50 feet 75. Domain is $\left(-\infty ,\infty \right)$. Range is $\left[-2,\infty \right)$. 77. Domain is $\left(-\infty ,\infty \right)$ Range is $\left(-\infty ,11\right]$. 79. $f\left(x\right)=2{x}^{2}-1$ 81. $f\left(x\right)=3{x}^{2}-9$ 83. $f\left(x\right)=5{x}^{2}-77$ 85. 50 feet by 50 feet. Maximize $f\left(x\right)=-{x}^{2}+100x$. 87. 125 feet by 62.5 feet. Maximize $f\left(x\right)=-2{x}^{2}+250x$. 89. 6 and –6; product is –36; maximize $f\left(x\right)={x}^{2}+12x$. 91. 2909.56 meters 93. \$10.70