Graph polynomial functions using zeros, factorizations, and end behavior.
Match a factored polynomial to its x-intercepts, multiplicities, and end behavior
Problem
For \(f(x)~=~(x~+~2)^2(x~-~1)\), state the \(x\text{-}\text{intercepts}\), whether the graph crosses or touches at \(\text{each}~\text{one}\), and the left and right end behavior.
Big Picture
What this problem is really about
Read the factored form in layers. The factor bases locate the intercepts, their exponents determine crossing or touching, and the combined degree with the leading sign determines the two tails. Check the features in that order so a correct intercept description is not paired with incompatible end behavior.
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