Warm Up Create the following… a cubic binomial a quadratic trinomial c) a 6th degree polynomial with 5 terms d) a quintic monomial with two different variables 2) Simplify (4x3 + 2x – 1) – (-8 + 2x + 9x3 + x4)

HW Check – pg 1

Zeros and End Behavior

The “zero” of a function is just the value at which a function touches the x-axis.

Factored Polynomial (x - 3) and (x + 5) are factors of the polynomial. It is easy to find the roots of a polynomial when it is in factored form! (x - 3) and (x + 5) are factors of the polynomial.

(x - 3) and (x + 5) are factors of the polynomial. (x - 3)(x + 5) = 0 (we want to know where the polynomial crosses the x-axis) So (x – 3) = 0 and (x + 5) = 0 The zeros are x = 3, x = -5

Practice: Find the roots of the following factored polynomials. y = (x-2)3(x+3)(x-4) y = (x-5)(x+2)3(x-14)2 y = (x+3)(x-15)4 y = x2(x+6)(x-6)

Sometimes the polynomial won’t be factored! Ex.

2nd → TRACE (CALC) → 2: zero

Choose a point to the left of the zero. Then press ENTER. This arrow indicates that you’ve chosen a point to the left of the zero.

Choose a point to the rightof the zero. Then press ENTER. This arrow indicates that you’ve chosen a point to the right of the zero.

Press ENTER one more time!

Find the zeros of the following polynomials:

Solutions

End Behavior The end behavior of a graph describes the far left and the far right portions of the graph. We can determine the end behaviors of a polynomial using the leading coefficient and the degree of a polynomial.

First determine whether the degree of the polynomial is even or odd. degree = 2 so it is even Next determine whether the leading coefficient is positive or negative. Leading coefficient = 2 so it is positive

Degree Even Odd Leading Coefficient + − High→High Low→High Low→Low

Find the end behavior of the following polynomials.