Question

What is the quadratic function that is created with roots -3 and 1 and a vertex at (-1, -8)?

Answer 1

hmm maybe not
you don't know that gives you the right vertex

Answer 2

That is the equation. It gives you the correct vertex, but I know that because of calculus.
A way to check w/o calc is to look at the values on either side. If the are the same, you have the correct vertex.

This is the only quadratic with those roots.