Question

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

Answer 1

once again, the vertex is at -a,b: where
y=(x+a)^2+b where the signs can be reversed

Answer 2

so you have the roots and can generalize the formula as:
(x+3)(x-1)a

Where a doesn't change the roots. To get the a correct, just plug in -1 for x and set it equal to 8. This well give you a quadratic containing the two roots and the point you want as the vertex.

Answer 3

so do
-8=(-1+3)(-1-1)a

Answer 4

@sylbot Thanks so much!

Answer 5

it actually doesn't even need to be the vertex, you can do it with the roots and ANY point using this method.

Answer 6

because the quadratic is distinct, the solution WILL give you an "a" that makes (-1,8) the vertex.