roots of polynomial functions agenda 9/24/2012 check hw collect composition of functions, inverses...

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

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

€

f (x) = x(x −1)(2x + 3).

Synonyms of

a “zero” x-intercept solution (when f(x) = 0) root

Roots of Polynomial Functions

A zero is a value of x that makes f(x) = 0.

Ex 2. Find the roots of

€

f (x) = x 3 − x 2 −6x

The Fundamental

Theorem of

Algebra

The degree of a polynomial P(x) is equal to the number of its zeros.

Roots of Polynomial Functions

A zero is a value

of x that makes f(x) = 0.Ex 3. Find the x-intercepts of

€

f (x) = 2x 3 + 4x 2 − 4x

Roots of Polynomial Functions

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

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

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P(t) = −0.00001t 3 +0.002t 2 +1.5t +100.

(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 = -5Xmax = 600Ymin = -5Ymax = 500

Roots of Polynomial Functions

Ex 4. The roots of a quadratic equation are x = 2, -3. Find the equation.

Zeros

FactorsIf 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

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

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