## anonymous one year ago HELP PLEASE ON PRECALC, Here's the question, help quickly and correctly and you shall receive a medal! lol: Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

1. anonymous

@phi

2. anonymous

Hello?

3. anonymous

4. anonymous

@phi can you help?

5. phi

First, plot the focus and vertex (roughly , need not be a work of art) can you do that?

6. anonymous

sure hold on

7. anonymous

actually no, can you? not sure where everything goes

8. phi

vertex is (0,0) and focus is (0,-7) can you plot these points?

9. anonymous

yep|dw:1437595113760:dw|

10. phi

and the parabola is a U shape the "curls around" the focus the vertex is the "tip" of the parabola. so it looks like this |dw:1437595121260:dw|

11. anonymous

ok so how do we get the equation now?

12. anonymous

uhoh

13. phi

the standard equation for the simplest parabola (with vertex at 0,0) is y= x^2 this one is upside down, so expect it to be y = - a x^2 to find y, we use the idea that 4 p y = x^2 is the equation of a parabola and "p" is the distance from the vertex to the focus

14. phi

in this case, the distance from -7 to 0 is 7 (ignoring the sign) 4p is 4*7= 28 so 28y= x^2 y = 1/28 x^2 but it has to be negative because we are upside down so $y = - \frac{1}{28} x^2$

15. anonymous

so for p i do this: $\left| -7 - 0 \right| = 7 so p = 7$

16. phi

that works

17. anonymous

oh ok. thanks can you help with one more. same type of problem, different info given

18. anonymous

Here it is: Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.

19. anonymous

i am going to draw it is that ok?

20. phi

yes, just to get an idea of what is going on.

21. anonymous

|dw:1437595918471:dw| it looks bad but i think that is the right idea?

22. anonymous

so what equation do i use for horizontal parabolas

23. phi

ok, except the vertex is exactly halfway between the directrix and focus

24. anonymous

oh ok so...

25. phi

you can just average the x values (-7+7)/2 = 0 the vertex is at (0,0) this one is sideways, so swap x and y in the standard 4py= x^2 to get 4p x = y^2 just like before p is the distance from the vertex to the focus

26. anonymous

which is 7 right? so p =7

27. anonymous

4(7)x = y^2?

28. anonymous

which simplifies to 28x = y^2, but that's not an answer choice. do you want to see them?

29. phi

ok

30. anonymous

y = (1/28)x^2 x = (1/28)y^2 -28y = x^2 y^2 = 14x

31. phi

28x = y^2 divide both sides by 28

32. anonymous

oh ok awesome! thanks so much!

33. phi

yw