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

1 Answer
Jun 4, 2017

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.