ET: 2.2a (Copy)

1. ET: 2.2a (Copy) Notes about graphs of polynomials Graph is continuous (Don’t have to pick up your pencil to draw it.) Graph is smooth Domain is all real numbers Notes about equations of polynomials An, an-1, an-2 are real numbers N must be a nonnegative integer (whole #) Degree of the polynomial is the highest value of n. • Look at page 139 • The graphs on the left are polynomials • The graphs on the right are not polynomials

2. More Parent Graphs f(x) = x4, x6, x8, …xeven} look like x2 f(x) = x5, x7, x9, …xodd} look like x3

3. Leading Coefficient Test

4. Zeros: If f(x) is degree n 

5. Find the zeros – Make a quick graph. Even Multiplicity: Touch x-axis Odd Multiplicity: Cross x-axis Act like y = +1x3 Leading Coefficient/ Parent Function

6. Find the zeros – Make a quick graph. At most how many zeros does f(x) have? x = 0 x = 3 4 f(x) is degree 4. Odd Multiplicity: Cross x-axis What function will f(x) resemble? y = -x4 parent function / leading coefficient

8. Roots of a 2nd degree polynomial are 2 and 3. Write a polynomial function that has the given zeros. f(x) = (x – 2)( x – 3) f(x) = -(x – 2)( x – 3) f(x) = 7(x – 2)( x – 3) Roots of a 3nd degree polynomial are 1 and -4. Write a polynomial function that has the given zeros. f(x) = (x – 1)( x + 4)2 f(x) = (x – 1)2( x + 4) f(x) = 3(x – 1)( x + 4)2

9. 5 is the only root of a 7th degree polynomial . Write a polynomial function that has the given zero. f(x) = (x – 5)7 f(x) = 4(x – 5)7 f(x) = -(x – 5)7 Roots of a 2nd degree polynomial are 1 and .Write a polynomial function that has the given zeros. f(x) = (x – 1)(x - )

10. Assignment 2.2 (Two Days: One Assignment worth double) 13-23 odd, 27-35, 41, 51, 56-57, 62, 66, 78, 79, 90, 97ab