Question

1. What is the equation of a parabola that has a vertex at (-2, 4) and goes through the point (0,8)?

Answer 1

y - k = (x + 2)^2

Explanation:

The vertex equation of a vertical parabola is

y - k = a(x - h)^2, where (h, k) is the vertex.

We are given h = -2, k = 4, x = 0 and y = 8 and need to find the value of a.

8 - 4 = a(0 + 2)^2, or

4 = 4a, so a must be 1.

Then the desired equation is:

y - k = (x + 2)^2