Give a possible formula of minimum degree for the polynomial f(x) in the graph below?

enter image source here

I know that my zeroes are (x+2) and (x-2) and y intercept is (0,-2) but I'm not sure how to write the "a"?

1 Answer
Nov 20, 2017

Please see below.

Explanation:

The graph does not cross the axis at 2, so 2 is a zero of even multiplicity. The minimum is multiplicity = 2 So (x-2)^2 is a factor.

And, as you have noted, x+2 is a factor.

f(x) = a(x+2)(x-2)^2

Use f(0) = a(2)(-2)^2 = -2 to see that a=-1/4