Question

What is the equation of the parabola that has a vertex at `(0, 16)` and passes through point `(2,20)`?

Answer 1

The equation is `y = x^2 + 16`

Explanation:

Recall vertex form of a parabola is given by

`y = a(x - p)^2 + q`

Where `(p, q)` is the vertex and `(x, y)` is a point which the parabola passes though. Therefore, we have enough information to solve for `a`.

`20 = a(2 - 0)^2 + 16`

`4 = a(4)`

`a = 1`

Therefore the equation of the parabola is `y = x^2 + 16`.

Hopefully this helps!