Question

Complete the general form equation of the parabola that passes through (4, -11) with vertex at : (2, -3).

Answer 1

Explanation:

You're given a coordinate in the form of (x, y) and you're also given the vertex in the form of (h, k). We will use those in the vertex form of the equation

`y=a(x-h)^2+k` and solve for a. Filling in:

`-11=a(4-2)^2-3` which simplifies a bit to

`-11=a(2)^2-3` and a bit more to

`-11=4a-3`. Add 3 to both sides to get

-8 = 4a so

a = -2

The equation, then, is

`y=-2(x-2)^2-3`