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

Question

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"?

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Answer 1 · 2017-11-20T01:52:23

Please see below.

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#