Question

Image: a steep curve with coordinate points of 1, 7 and -3, 7 with the final coordinate of -1, -1.


write the equation for the graph in vertex form.

The equation is not: y = 2(x + 1)^2 - 1.

Answer 1

Vertex form is y = a(x − h)^2 + k. With vertex (h,k) = (−1, −1) that gives

y = a(x + 1)^2 − 1.

Use one of the other points, say (1,7), to find a:
7 = a(1 + 1)^2 − 1 = 4a − 1 ⇒ 4a = 8 ⇒ a = 2.

So the equation is
y = 2(x + 1)^2 − 1.

Check with (−3,7): 2(−3+1)^2 − 1 = 2(4) − 1 = 7, so it matches. (Expanded form: y = 2x^2 + 4x + 1.) If you meant different points or the graph looks different, tell me and I’ll recheck.