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Overview
Grade 12 Pre-Calculus Mathematics (40S)
Develop algebraic and graphical reasoning through the study of relations
22. Graph and analyze polynomial functions
22.2 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
MB Curriculum Aligned