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Polynomial Functions Graphing - Multiplicity, End Behavior, Finding Zeros - Precalculus & Algebra 2. Module 8: Determining the Zeros (and Their Multiplicity) of a Polynomial Graphically.

We call this a triple zero, or a zero with multiplicity 3. For zeros with even multiplicities, the graphs touch or are tangent to the x-axis at these x-values. For zeros with odd multiplicities, the graphs cross or intersect the x-axis at these x-values. See the graphs below for examples of graphs of polynomial functions with multiplicity 1, 2 ...

Given a quadratic equation, the student will make connections among the solutions (roots) of the quadratic equation, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

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zeros of the function will be less than or equal to the number of complex zeros. 3. The real zeros of a polynomial function may be found by factoring (where possible) or by finding where the graph touches the x-axis. The number of times a zero occurs is called its multiplicity. If a function has a zero of odd multiplicity, the graph of the

5th Grade Math - Fluency with fraction addition and subtraction, improve skill with fraction multiplication and division, decimal operations, developing understanding of volume.