Solutions to Try Its

1. Focus: $\left(-4,0\right)$; Directrix: $x=4$; Endpoints of the latus rectum: $\left(-4,\pm 8\right)$

2. Focus: $\left(0,2\right)$; Directrix: $y=-2$; Endpoints of the latus rectum: $\left(\pm 4,2\right)$.

3. ${x}^{2}=14y$

4. ${x}^{2}=14y$

5. Vertex: $\left(8,-1\right)$; Axis of symmetry: $y=-1$; Focus: $\left(9,-1\right)$; Directrix: $x=7$; Endpoints of the latus rectum: $\left(9,-3\right)$ and $\left(9,1\right)$.

6. Vertex: $\left(-2,3\right)$; Axis of symmetry: $x=-2$; Focus: $\left(-2,-2\right)$; Directrix: $y=8$; Endpoints of the latus rectum: $\left(-12,-2\right)$ and $\left(8,-2\right)$.

7.  a. ${y}^{2}=1280x$
b. The depth of the cooker is 500 mm

Solutions to Odd-Numbered Exercises

1. A parabola is the set of points in the plane that lie equidistant from a fixed point, the focus, and a fixed line, the directrix.

3. The graph will open down.

5. The distance between the focus and directrix will increase.

7. yes $y=4\left(1\right){x}^{2}$

9. yes ${\left(y - 3\right)}^{2}=4\left(2\right)\left(x - 2\right)$

11. ${y}^{2}=\frac{1}{8}x,V:\left(0,0\right);F:\left(\frac{1}{32},0\right);d:x=-\frac{1}{32}$

13. ${x}^{2}=-\frac{1}{4}y,V:\left(0,0\right);F:\left(0,-\frac{1}{16}\right);d:y=\frac{1}{16}$

15. ${y}^{2}=\frac{1}{36}x,V:\left(0,0\right);F:\left(\frac{1}{144},0\right);d:x=-\frac{1}{144}$

17. ${\left(x - 1\right)}^{2}=4\left(y - 1\right),V:\left(1,1\right);F:\left(1,2\right);d:y=0$

19. ${\left(y - 4\right)}^{2}=2\left(x+3\right),V:\left(-3,4\right);F:\left(-\frac{5}{2},4\right);d:x=-\frac{7}{2}$

21. ${\left(x+4\right)}^{2}=24\left(y+1\right),V:\left(-4,-1\right);F:\left(-4,5\right);d:y=-7$

23. ${\left(y - 3\right)}^{2}=-12\left(x+1\right),V:\left(-1,3\right);F:\left(-4,3\right);d:x=2$

25. ${\left(x - 5\right)}^{2}=\frac{4}{5}\left(y+3\right),V:\left(5,-3\right);F:\left(5,-\frac{14}{5}\right);d:y=-\frac{16}{5}$

27. ${\left(x - 2\right)}^{2}=-2\left(y - 5\right),V:\left(2,5\right);F:\left(2,\frac{9}{2}\right);d:y=\frac{11}{2}$

29. ${\left(y - 1\right)}^{2}=\frac{4}{3}\left(x - 5\right),V:\left(5,1\right);F:\left(\frac{16}{3},1\right);d:x=\frac{14}{3}$

31. 

33.

35.

37.

39.

41.

43. 

45. ${x}^{2}=-16y$

47. ${\left(y - 2\right)}^{2}=4\sqrt{2}\left(x - 2\right)$

49. ${\left(y+\sqrt{3}\right)}^{2}=-4\sqrt{2}\left(x-\sqrt{2}\right)$

51. ${x}^{2}=y$

53. ${\left(y - 2\right)}^{2}=\frac{1}{4}\left(x+2\right)$

55. ${\left(y-\sqrt{3}\right)}^{2}=4\sqrt{5}\left(x+\sqrt{2}\right)$

57. ${y}^{2}=-8x$

59. ${\left(y+1\right)}^{2}=12\left(x+3\right)$

61. $\left(0,1\right)$

63. At the point 2.25 feet above the vertex.

65. 0.5625 feet

67. ${x}^{2}=-125\left(y - 20\right)$, height is 7.2 feet

69. 2304 feet