What is an equation of a parabola with the given vertex and focus? vertex: (–2, 5); focus: (–2, 6)

Question

What is an equation of a parabola with the given vertex and focus?  vertex: (–2, 5); focus: (–2, 6)

anonymous · Answer

First you wanna use: $$
x^2 = 4py
$$Where $p$ is the distance between the focus and the vertex.

anonymous · Answer

his will give you a parabola that is centered at the origin.

anonymous · Answer

Then you want to translate it by replacing $y$ with $(y-k)$ and $x$ with $(x-h)$, where the vertex is $(h,k)$

anonymous · Answer

then what?? @wio

anonymous · Answer

Do all that and you're left with a parabola.

anonymous · Answer

what equation do i use to find it out?

anonymous · Answer

$p$ is the distance from the vertex and focus, in this case it is $1$.
So we start out with $$
x^2=4(1)y = 4y \implies y= \frac{x^2}{4}
$$

anonymous · Answer

Then we translate our parabola into the correct vertex. $$
y - 5 = \frac{(x-(-2))^2}{4} = \frac{(x+2)^2}{4}\implies y = \frac{1}{4}(x+2)^2+5
$$Then foil

anonymous · Answer

soo would that be the answer? @wio