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Today in Pre-Calculus

Review homework, explore end behavior of polynomial functions, find zeros, understand graph behavior, and prepare for upcoming quiz.

stevepugh
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Today in Pre-Calculus

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  1. Today in Pre-Calculus • Go over homework • Notes: (need calculator & book) • Graphs of Polynomial Functions • End Behavior • Zeros • Homework

  2. End Behavior of Polynomial Functions Page 203 Exploration 1 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: Tuesday, October 30

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