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#.