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Warm Up 1.Write the standard form of the quadratic function given a vertex and a point: vertex : (-4,-1) point: (-2,4) 2. State the vertex of the following function: F(x) = x 2 - 7

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Math IV Lesson 8 Polynomial functions of higher degrees Essential Question: How do you sketch graphs of polynomial functions? Standard: MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

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1. Continuous- a graph that has no breaks, holes, or gaps. 2. Leading coefficient test- is used to determine the end behavior of a polynomial function. 3. Zero- a zero of a function f is a number x such that f(x) = Relative extrema- maximas and minimas

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Leading coefficient test

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1. a function f of highest degree n has at most n real zeros. 2. The graph f of highest degree n has at most n-1 relative extrema (max or min)

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Find all of the zeros of the polynomial function. (hint: factor) F(x) = x 3 –x 2 -2x 0 = x 3 –x 2 -2x 0 = x (x 2 –x -2) 0 = x (x-2)(x+1) X = 0 x – 2 = 0 x + 1 = 0 X = 0 x = 2 x = -1 Zeros are 0, 2, and -1

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Repeated zeros For a polynomial function a factor (x-a) k, k > 1 yields a repeated zero x = a of multiplicity k. 1.If K is odd, the graph crosses at that zero. 2.If k is even, the graph touches at that zero. Example: F(x) = (x-2) 2 (x+4) 3 x – 2 = 0 x + 4 = 0 X = 2 x = -4 Mult = 2 mult = 3 Touches crosses

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