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Today in Pre-Calculus

Today's lesson covers end behavior and zeros of polynomial functions. Learn how to describe end behavior of odd and even degree polynomials, find zeros, and understand multiplicity. Homework and quiz details included.

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Today in Pre-Calculus

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  1. Today in Pre-Calculus • Go over homework • Notes: Graphs of Polynomial Functions • End Behavior • Zeros • Homework

  2. End Behavior of Polynomial Functions If degree of polynomial is odd If degree of polynomial is even If leading coefficient is negative: graph reflects over x-axis so the end behavior changes signs.

  3. End Behavior of Polynomial Functions Examples: Describe the end behavior of the following functions without graphing them. 1) f(x) = x3 + 2x2 – 11x – 12 2) g(x) = –2x4 + 2x3 – 22x2 – 18x + 35

  4. Finding Zeros of Polynomial Functions Example: Find the zeros of f(x) = 5x3 – 5x2 – 30x 5x3 – 5x2 – 30x = 0 set equal to zero 5x(x2 – x – 6) = 0 factor GCF 5x(x – 3)(x + 2) = 0 factor 5x = 0 x – 3 = 0 x + 2 = 0 set EVERY term = 0 x = 0, 3, -2 solve for x

  5. Multiplicity of a Zero If f is a polynomial function and (x – c)m is a factor of f, then c is a zero of multiplicity m. (c is a repeated zero). Example: f(x) = (x – 2)3(x+1)2 If the multiplicity is odd, then the graph crosses the x-axis at (c,0) and the value of f changes sign at x = c If the multiplicity is even, then the graph touches (but does not cross) the x-axis at (c,0) and the value of f does NOT change sign at x = c

  6. Homework • Pg. 209: 9-12, 26-28, 34, 36, 39-41 • Quiz: Monday, November 2

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