See Problem 3.

23. Optics A cross section of a flashlight reflector is a parabola. The bulb is located at the focus. Suppose the bulb is located 1 4 1 fourth  in. from the vertex of the reflector. Model a cross section of the reflector by writing an equation of a parabola that opens upward and has its vertex at the origin. What is an advantage of this parabolic design?

See Problem 4.

Identify the vertex, the focus, and the directrix of the parabola with the given equation. Then sketch the graph of the parabola.

24. y = x 2 + 4 x + 3 y equals , x squared , plus 4 x plus 3
25. y = x 2 − 6 x + 11 y equals , x squared , minus 6 x plus 11
26. y = x 2 + 8 x + 13 y equals , x squared , plus 8 x plus 13
27. y = x 2 − 2 x − 4 y equals , x squared , minus 2 x minus 4
28. y = x 2 − 8 x + 17 y equals , x squared , minus 8 x plus 17
29. y = 2 x 2 + 4 x − 2 y equals , 2 x squared , plus 4 x minus 2

See Problem 5.

Write an equation of a parabola with the given vertex and focus.

30. vertex (4, 1), focus (6, 1)
31. vertex (0, 3), focus ( − 8 , 3 ) open negative 8 comma 3 close
32. vertex ( − 5 , 4 ) , negative 5 comma 4 close comma  focus ( − 5 , 0 ) negative 5 comma 0 close
33. vertex (7, 2), focus ( 7 , − 2 ) open 7 comma negative 2 close

B Apply

Identify the vertex, the focus, and the directrix of a parabola with each equation. Then sketch a graph of the parabola with the given equation.

34. y 2 − 25 x = 0 y squared , minus 25 x equals 0
35. x 2 = − 4 y x squared , equals negative 4 y
36. ( x − 2 ) 2 = 4 y open x minus 2 close squared . equals 4 y
37. − 8 x = y 2 negative 8 x equals , y squared
38. y 2 − 6 x = 18 y squared , minus 6 x equals 18
39. x 2 + 24 y − 8 x = − 16 x squared , plus 24 y minus 8 x equals negative 16

40. Think About a Plan In some solar collectors, a mirror with a parabolic cross section is used to concentrate sunlight on a pipe, which is located at the focus of the mirror as shown in the diagram. What is an equation of the parabola that models the cross section of the mirror?

    

    • What information can you get from the diagram?
    • What information do you need to be able to write an equation that models the cross section of the mirror?
41. Earth Science The equation d = 1 10 s 2 d equals , 1 tenth , s squared  relates the depth d (in meters) of the ocean to the speed s (in m/s) at which tsunamis travel. What is the graph of the equation?

Use the information in each graph to write the equation for the parabola.

42. 
43. 
44. 
45. Sound Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of 28 inches and a depth of 14 inches. If the receiver of the microphone is located at the focus of the reflector dish, how far from the vertex should the receiver be positioned?

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