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Overview
Foundations of Mathematics 12 (MAT621A)
Relations and Functions
6. Represent data using polynomial functions of degree ≤ 3 to solve problems
6.2 Characteristics of polynomial graphs
Characteristics of Polynomial Graphs
Zeros, turning points, and end behavior -- three features you can read directly from a polynomial's equation.
What You'll Learn
Zeros are where the graph crosses the x-axis -- the polynomial's roots.
Turning points are local highs and lows; a degree-n polynomial has at most n-1.
End behavior (far left and far right) is controlled by the leading term.
Odd-degree, positive-leading-coefficient graphs fall left and rise right.
Even-degree polynomials point the same direction on both ends.
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
Learning resources
Skills
Polynomial Graphs
Leading Coefficient
Degree of Polynomial
End Behavior
X-Intercepts
Y-Intercepts
Graphing
Factoring
PEI Curriculum Aligned