Question

Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1).

Answer 1

Will you help me DebbieG?

Answer 2

Each root c means that there is a factor x-c. so you can "cook up" a polynomial with the roots a and b by taking the product:

(x-a)(x-b)

Answer 3

That handles getting the roots that you want. Now for the vertex, the roots sort of "pin down" the x-coordinate.... here's why:

A parabola is symmetric about it's axis of symmetry, right? So necessarily, the x-coordinate of the vertex HAS to lie HALFWAY between the 2 roots.

But the y-coordinate can be "fiddled with" by simply multiplying the whole polynomial by whatever factor it takes to get the desired y-coordinate.

Answer 4

So what is the answer?

Answer 5

These have the same roots, same x-coodinate of the vertex, but different y-coordinates for the vertex.