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Sec 3.1 Polynomials and Their Graphs (std MA 6.0)

Sec 3.1 Polynomials and Their Graphs (std MA 6.0). Objectives: To determine left and right end behavior of a polynomial. To find the zeros of a polynomial by factoring. Determining left and right end behavior of a polynomial.

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Sec 3.1 Polynomials and Their Graphs (std MA 6.0)

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  1. Sec 3.1 Polynomials and Their Graphs (std MA 6.0) Objectives: To determine left and right end behavior of a polynomial. To find the zeros of a polynomial by factoring.

  2. Determining left and right end behavior of a polynomial. To determine the left and right end behavior of a polynomial we need to look at two things. The leading coefficient of the function. The degree of the function. Recall xn and –xn.

  3. We can summarize our findings in a table.

  4. Ex 1. For the following graphs determine the left and right behavior of the graph. • y = 3x2+4x-6 • y = -3x3+5x-8 • y = x5-4x3+5 • y = -2x4 + x3-2x2+6x-18 • y =(x-2)(x+1)(x+2)

  5. Zeros of a Polynomial Function If P is a polynomial and c is a real number, then the following are true. • c is a zero of P. • x = c is a solution of the equation P(x) = 0. • x – c is a factor of P(x). • x = c is an x-intercept of the graph of P.

  6. Ex 1. Find the zeros of P(x) = x2 + x – 6 by factoring.

  7. Ex 2. Find the zeros by factoring. • P(x) = x3 – 3x2 – 10x • b) P(x) = x4 + x3 – 8x - 8

  8. Ex 3. Find the zeros and determine the end behavior of each graph. a) b) c)

  9. Class Work Find the zeros and determine the end behavior. 1. P(x)= -2x(x – 6) 2. P(x) = 9x2 + 18x -7 3. P(x)= (x-3)(x+4)(x-8)(x+7) 4. P(x) = 2x3 - 4x2 – 16x

  10. HW #1 p262 1-3(describe the transformations) 5-10 all, 11-35 odd (find zeros and find end behavior)

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