Back to Identify zeros and graph polynomials — Problem 4 · Task Set 14

Exercises: Identify Zeros and Graph Polynomials

Work through each section in order. For graph-related problems, describe behavior in terms of crossing, bouncing, and end behavior arrows.

Grade 9·22 problems·~38 min·Common Core Math - HS Algebra·standard·hsa-apr-b-3

Work through problems with immediate feedback

Fluency Practice

$Two side-by-side graphs: left shows p(x) crossing through both x-intercepts; right shows q(x) bouncing at x=4 (even multiplicity) while still crossing at x=-1.$

For $p(x) = (x - 4)^2(x + 1)$ , what does the graph do at $x = 4$ ?

The graph crosses the x-axis at $x = 4$ because 4 is positive.

The graph crosses the x-axis at $x = 4$ because all zeros cause crossing.

The graph bounces (touches without crossing) at $x = 4$ because the multiplicity is 2 (even).

The graph has no x-intercept at $x = 4$ because $(x - 4)^2 \geq 0$ always.