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2.2 Polynomial Functions of Higher Degree

2.2 Polynomial Functions of Higher Degree. Note: We will be talking about continuous functions in 3.2. f(x) = ax n where n. If n is odd and a > 0, then f(x) will end in Quad’s I & III. If n is odd and a < 0, then f(x) will end in Quad’s II & IV.

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2.2 Polynomial Functions of Higher Degree

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  1. 2.2 Polynomial Functions of Higher Degree Note: We will be talking about continuous functions in 3.2 f(x) = axn where n If n is odd and a > 0, then f(x) will end in Quad’s I & III If n is odd and a < 0, then f(x) will end in Quad’s II & IV If n is even and a > 0, then f(x) will end in Quad’s I & II If n is even and a < 0, then f(x) will end in Quad’s III & IV

  2. What quadrants will the following functions finish in? f(x) = -x3 +4x f(x) = x4 – 5x2 + 4 f(x) = x5 – x f(x) = -x2 + 4x - 7 II & IV I & II I & III III & IV

  3. A zero of a function f is an x-value for which f(x) = 0. In other words, zeros are the x-intercepts orsolutions of the polynomial f(x) = 0. Ex. Find the real zeros of f(x) = x3 – x2 – 2x Graph 0 = x3 – x2 – 2x 0 = x(x2 – x – 2) 0 = x(x – 2)(x + 1) 0, 2, -1 are the real zeros. + x3 means it ends in what quadrants? I, III

  4. Ex. Find the real zeros of f(x) = -2x4 + 2x2 0 = -2x4 + 2x2 0 = -2x2(x2 – 1) 0 = -2x2(x – 1)(x + 1) zeros 0, 1, -1 what quadrants does a -x4 end up in? III, IV

  5. Ex. Find a polynomial with the given zeros. a. -2, -1, 1, 2 f(x) = (x + 2)(x + 1)(x – 1)(x – 2) Foil these first f(x) = (x2 – 4)(x2 – 1) f(x) = x4 – 5x2 + 4 (x + ½) or (2x + 1) b. -1/2, 3, 3 f(x) = (2x + 1)(x – 3)(x – 3) f(x) = (2x + 1)(x2 – 6x + 9) f(x) = 2x3 – 11x2 + 12x + 9

  6. Use the Intermediate Value Theorem to approximate the real zero of f(x) = x3 – x2 + 1 Use graphing calculator to graph f(x) and then use the table to find the zero.

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