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