1 / 7

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.

maxwell-allen
Download Presentation

2.2 Polynomial Functions of Higher Degree

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related