Question

Need Help.

write an equation of a parabola with vertex at the origin and the given focus (0 -5)

Answer 1

The origin is (0,0)

Answer 2

is the focus above or below the vertex?

Answer 3

Above?

Answer 4

Vertex: (0,0)

Focus: (0,-5)

Answer 5

is the focus above or below the vertex?

Answer 6

Below?

Answer 7

yes

Answer 8

what is the vertical distance from the focus to the vertex?

Answer 9

-5 units? I'm not sure, lol not very good at match at all!

Answer 10

distance is never negative

Answer 11

it's actually +5 or just 5

Answer 12

so that means the focal distance, p, is

p = 5

Answer 13

Oh ok. I'll remember that.

Answer 14

the vertex is (h,k) = (0,0)

so,

h = 0
k = 0

Answer 15

plug p = 5, h = 0, and k = 0 into

4p(y-k) = (x-h)^2

and solve for y. Tell me what you get.

Answer 16

20y-20=x^2-0?

Answer 17

k = 0, not k = 1

Answer 18

oh duh.. so 20y-0=x^2-0?

Answer 19

that's the same as 20y = x^2

then you can solve for y to get y = ???

Answer 20

1/20x^2?? I have no idea... I'm drawing a blank.

Answer 21

yes, correct

now because the focus is below the vertex, this means the parabola opens downward

so the leading coefficient is negative making the final answer to be

\[\Large y = -\frac{1}{20}x^2\]

Answer 22

Okay!! Thank you so much!! You helped a lot!

Answer 23

you're welcome