What is the equation of the parabola that has a vertex at (4, 2) and passes through point (6,34) ?

1 Answer
Apr 25, 2018

y = 8(x-4)^2+2

Explanation:

When the parabola has a vertex at (4,2) its equation looks like y= a(x-4)^2+2 and we plug in (6,34) to find a:

34=a(6-4)^2+2

32=4a

a=8

So we get

y = 8(x-4)^2+2

We could expand this into standard form, but at this point we've answered the question so let's stop.

Check: The vertex is correct by construction.

8(6-4)^2 +2 = 8(4)+2 = 34 quad sqrt