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Chapter 27.7
Characteristics of polynomial graphs
What You'll Learn
Identify how the leading coefficient sign determines whether the right arm points up or down
Determine graph behavior using the degree of a polynomial (even vs. odd)
Recognize that positive leading coefficients point upward and negative ones point downward
Apply the arm direction rules: even degree means both arms go the same way, odd means opposite
Find x-intercepts by setting factored polynomial expressions equal to zero
Calculate y-intercepts by substituting x = 0 into the polynomial function
What You'll Practice
1
Matching polynomial expressions to their corresponding graphs
2
Sketching polynomial graphs from factored form using intercepts and arm behavior
3
Identifying quartic and cubic functions by their visual characteristics
4
Factoring polynomial expressions to find x-intercepts before graphing
Why This Matters
Understanding polynomial graph characteristics helps you visualize equations and predict function behavior without a calculator. This skill is essential for calculus, where analyzing function behavior, limits, and end behavior depends on recognizing these patterns quickly.
Before You Start — Make Sure You Can:
This Unit Includes
6 Video lessons
Skills
Polynomial Graphs
Leading Coefficient
Degree of Polynomial
End Behavior
X-Intercepts
Y-Intercepts
Graphing
Factoring
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