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

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1 Answer
Dean R.
Jun 22, 2018

# h(x) =1/15 (x +3)(x-3)(x+1)(x-1)^2#

We got the factors from the zeros. It's odd degree since it has both #+infty# and #-infty# as ends. #x=1# is tangent, so we squared #x-1.# At #x=2# we have #(2-3)(2+3)(2+1)(2-1)^2=-15# and we want #h(2)=-1# so we multiply by #1/15.#

Explanation:

graph{1/15 (x +3)(x-3)(x+1)(x-1)^2 [-10, 10, -5, 5]}

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