Question

What is the equation of the parabola that has a vertex at `(-1, 16)` and passes through point `(3,32)`?

Answer 1

`y-16 = (x+1)^2`

Explanation:

A parabola with vertex `(h,k)` has an equation of the form:

#y=h=a(x-k)^2.

So this parabola is `y-16=a(x_1)^2`.

Using the fact that when `x=-1`, we have `y = 32` we can find `a`.

`32 - 16 = a(3+1)^2`

So `a = 1`