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

$y = 2 {\left(x - 12\right)}^{2} + 4$
You can use vertex form, $y = a {\left(x - h\right)}^{2} + k$, 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 $54 = a {\left(7 - 12\right)}^{2} + 4$.
Simplify inside the parabola first to get $54 = a {\left(- 5\right)}^{2} + 4$, then do the exponent to get $54 = 25 a - 4$.
Subtract 4 from both sides in order to isolate the variable and get $50 = 25 a$.
Divide both sides by 25 to get $a = 2$, and then plug this back into vertex form to get the equation $y = 2 {\left(x - 12\right)}^{2} + 4$.