Pre-Cal
1. Find the equation of a parabola with vertex (2, -1), opens upward and has focal width of 16.
2. Find the equation of a parabola with focus (2, -3) and directrix x = 5.

Step-by-step explanation:

1. For a parabola with vertex (h, k) that opens upward, the equation can be written ...

  y = 1/(4p)(x -h)^2 +k

where 4p is the focal width. Here, that is 16, and (h, k) = (2, -1), so the equation is ...

  y = 1/16(x -2)^2 -1

__

2. The focal width is 4 times the distance from the focus to the directrix, so for this one we have ...

  4p = 4(2 -5) = -12

Because the parabola opens sideways, the roles of x and y in the equation are swapped. The equation for this parabola is ...

  x = 1/(4p)(y -k)^2 +h . . . . . . . for vertex (h, k) and focal width 4p

  x = -1/12(y +3)^2 +2

_____

The graph shows the two parabolas and their equations. The dashed lines are the focal width and the directrix.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

898.1666667

step-by-step explanation:

5389/6 = 898.1666667