Question

What is the equation of the parabola that has a vertex at `(12, 4)` and passes through point `(7,54)`?

Answer 1

`y=2(x-12)^2+4`

Explanation:

You can use vertex form, `y=a(x-h)^2+k`, to solve for the equation. The vertex of the parabola being (h,k) and the given point being (x,y), so that h=12, k=4, x=7, and y=54.
Then just plug it in to get `54=a(7-12)^2+4`.
Simplify inside the parabola first to get `54=a(-5)^2+4`, then do the exponent to get `54=25a-4`.
Subtract 4 from both sides in order to isolate the variable and get `50=25a`.
Divide both sides by 25 to get `a=2`, and then plug this back into vertex form to get the equation `y=2(x-12)^2+4`.