Question

What is the equation of the following graph in vertex form?

(-4, 0)
(-2, 0)
(-3,-1)

Answer 1

y = (x+3)^2 -1

Explanation:

The vertex among the given points is (-3, -1). The other two points are symmetrical about this one. For a difference from the vertex of Δx = 1, the y-values are 1 more than at the vertex: (0 -(-1)) = 1. This means the scale factor is 1.

The vertex form is ...

y = a(x -h)^2 +k

for vertical scale factor a and vertex (h, k). You have a=1, (h, k) = (-3, -1), so your equation is ...

y = (x +3)^2 -1