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