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Building Skills

9. f
11. a
13. h
15. g
17. $y = - 2 x^{2}$ $y = - 2 x^{2}$
19. $y = 5 x^{2}$ $y = 5 x^{2}$
21. $y = 2 x^{2}$ $y = 2 x^{2}$
23. $y = - {(x + 3)}^{2}$ $y = - {(x + 3)}^{2}$
25. $y = 2 {(x - 2)}^{2} + 5$ $y = 2 {(x - 2)}^{2} + 5$
27. $y = \frac{11}{49} {(x - 2)}^{2} - 3$ $y = \frac{11}{49} {(x - 2)}^{2} - 3$
29. $y = - 12 {(x - \frac{1}{2})}^{2} + \frac{1}{2}$ $y = - 12 {(x - \frac{1}{2})}^{2} + \frac{1}{2}$
31. $y = \frac{3}{4} {(x + 2)}^{2}$ $y = \frac{3}{4} {(x + 2)}^{2}$
33. $y = \frac{3}{4} {(x - 3)}^{2} - 1$ $y = \frac{3}{4} {(x - 3)}^{2} - 1$
35.

The graph is the graph of $y = x^{2}$ $y = x^{2}$ stretched vertically by a factor of 3.
37.

The graph is the graph of $y = x^{2}$ $y = x^{2}$ shifted 4 units to the right.
39.

The graph is the graph of $y = x^{2}$ $y = x^{2}$ stretched vertically by a factor of 2, reflected about the x-axis, and shifted down 4 units.
41.

The graph is the graph of $y = x^{2}$ $y = x^{2}$ shifted 3 units right and 2 units up.
43. The graph is the graph of $y = x^{2}$ $y = x^{2}$ shifted 2 units right, stretched vertically by a factor of 3, reflected about the x-axis, and shifted 4 units up.
45. $y = {(x + 2)}^{2} - 4 .$ $y = {(x + 2)}^{2} - 4 .$ The graph is the graph of $y = x^{2}$ $y = x^{2}$ shifted 2 units to the left and 4 units down. Vertex: $(- 2, - 4);$ $(- 2, - 4);$ axis: $x = - 2;$ $x = - 2;$ x-intercepts: $- 4$ $- 4$ and 0; y-intercept: 0
47. $y = - {(x - 3)}^{2} - 1 .$ $y = - {(x - 3)}^{2} - 1 .$ The graph is the graph of $y = x^{2}$ $y = x^{2}$ shifted 3 units to the right, reflected about the x-axis, and shifted 1 unit down. Vertex: $(3, - 1);$ $(3, - 1);$ axis: $x = 3;$ $x = 3;$ no x-intercept; y-intercept: $- 10$ $- 10$
49. $y = 2 {(x - 2)}^{2} + 1 .$ $y = 2 {(x - 2)}^{2} + 1 .$ The graph is the graph of $y = x^{2}$ $y = x^{2}$ shifted 2 units to the right, stretched vertically by a factor of 2, and shifted 1 unit up.

Vertex: (2, 1) axis: $x = 2;$ $x = 2;$ no x-intercept; y-intercept: 9
51. $y = - 3 {(x - 3)}^{2} + 16 .$ $y = - 3 {(x - 3)}^{2} + 16 .$ The graph is the graph of $y = x^{2}$ $y = x^{2}$ shifted 3 units to the right, stretched vertically by a factor of 3, reflected about the x-axis, and shifted 16 units up.

Vertex: (3, 16); axis: $x = 3;$ $x = 3;$ x-intercepts: $3 \pm \frac{4}{3} \sqrt{3};$ $3 \pm \frac{4}{3} \sqrt{3};$ y-intercept: $- 11$ $- 11$
53. $y = - {(x + 2)}^{2} + 4$ $y = - {(x + 2)}^{2} + 4$ . The graph of $y = x^{2}$ $y = x^{2}$ is shifted 2 units to the left, reflected about the x-axis, and then shifted 4 units up. Vertex: $(- 2, 4)$ $(- 2, 4)$ ; axis: $x = - 2$ $x = - 2$ ; x-intercepts: $- 4$ $- 4$ and 0; y-intercept: 0.
55.
1. Opens up
2. $(4, - 1)$ $(4, - 1)$
3. $x = 4$ $x = 4$
4. x-intercepts: 3 and 5; y-intercept: 15
57.
1. Opens up
2. $(\frac{1}{2}, \frac{- 25}{4})$ $(\frac{1}{2}, \frac{- 25}{4})$
3. $x = \frac{1}{2}$ $x = \frac{1}{2}$
4. x-intercepts: $- 2 and 3;$ $- 2 and 3;$ y-intercept: $- 6$ $- 6$
59.
1. Opens up
2. (1, 3)
3. $x = 1$ $x = 1$
4. x-intercepts: none; y-intercept: 4
61.
1. Opens down
2. $(- 1, 7)$ $(- 1, 7)$
3. $x = - 1$ $x = - 1$
4. x-intercepts: $- 1 \pm \sqrt{7};$ $- 1 \pm \sqrt{7};$ y-intercept: 6
63.
1. Minimum: $- 1$ $- 1$
2. $[- 1, \infty)$ $[- 1, \infty)$
65.
1. Maximum: 0
2. $(- \infty, 0]$ $(- \infty, 0]$
67.
1. Minimum: $- 5$ $- 5$
2. $[- 5, \infty)$ $[- 5, \infty)$
69.
1. Maximum: 16
2. $(- \infty, 16]$ $(- \infty, 16]$
71.

Solution: $[- 2, 2]$ $[- 2, 2]$
73.

Solution: $(- \infty, 1) \cup (3, \infty)$ $(- \infty, 1) \cup (3, \infty)$
75.

Solution: $(- 1, \frac{7}{6})$ $(- 1, \frac{7}{6})$