1. Roots of Polynomial Functions Agenda 9/24/2012 Check HW Collect Composition of Functions, Inverses HW notes: Factors  Zeros Matching Activity Turkey Problem notes: Zeros  Factors

2. Roots of Polynomial Functions I. Zeros of Polynomials A zero is a value of x that makes f(x) = 0. Ex 1. Find the zeros of Synonyms of a “zero” x-intercept solution (when f(x) = 0) root

3. Roots of Polynomial Functions A zero is a value of x that makes f(x) = 0. Ex 2. Find the roots of The Fundamental Theorem of Algebra The degree of a polynomial P(x) is equal to the number of its zeros.

4. Roots of Polynomial Functions A zero is a value of x that makes f(x) = 0. Ex 3. Find the x-intercepts of

5. Roots of Polynomial Functions A zero is a value of x that makes f(x) = 0. MATCHING.

6. Roots of Polynomial Functions Stephanie, a biologist who does research for the poultry industry, models the population P of wild turkeys, t days after being left to reproduce with the function (b)Find what the maximum turkey population is and when it occurs. (c)Assuming that the model continues to be accurate, when will this turkey population become extinct? *What scenarios could explain the growth exhibited by this turkey population? (a)Graph the function. Change WINDOW settings Xmin = -5 Xmax = 600 Ymin = -5 Ymax = 500

7. Roots of Polynomial Functions Ex 4. The roots of a quadratic equation are x = 2, -3. Find the equation. Zeros  Factors If x = k is a zero of the polynomial P(x), then (x – k) is a factor of P(x). 1. Convert roots  factors 2. Write as a product of binomials. 3. FOIL/BOX & CLT

8. Roots of Polynomial Functions Ex 5. The x-intercepts of a polynomial are x = 0, ½, 3. Find the equation of this polynomial. If x = k is a zero of the polynomial P(x), then (x – k) is a factor of P(x). 1. Convert roots  factors 2. Write as a product of binomials. 3. FOIL/BOX & CLT

9. Roots of Polynomial Functions Ex 6. The zeros of a polynomial are x = 1, -2, 4. Find the equation of this polynomial. If x = k is a zero of the polynomial P(x), then (x – k) is a factor of P(x). 1. Convert roots  factors 2. Write as a product of binomials. 3. FOIL/BOX & CLT