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A-APR.3 Warmup M3-003-A06-V01

Identify zeros from factorizations and use them to sketch polynomial graphs.

Match a factored polynomial to its graph using zeros, multiplicities, and end behavior

Problem

Match \((x~+~1)^2(x~-~3)\) to a graph using its zero behavior and end behavior.

Four graph options share zeros -1 and 3. Option A touches at -1, crosses at 3, and has left-down/right-up ends. Option B crosses at -1, touches at 3, and has left-down/right-up ends. Option C touches at -1, crosses at 3, and has left-up/right-down ends. Option D crosses at both zeros and has both ends rising. Open full size
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What this problem is really about

The factorization gives three independent filters for the graph. First locate each zero; then use the exponent on its factor to predict a crossing or a bounce. Finally, combine the total degree with the sign of the leading coefficient to predict the two tails, and keep only a graph that satisfies all three checks.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
A-APR.3
Category
Algebra
Domain
Arithmetic with Polynomials and Rational Expressions
Objective
Identify zeros from factorizations and use them to sketch polynomial graphs.
Problem type
Match a factored polynomial to its graph using zeros, multiplicities, and end behavior