Students should be able to…

› Evaluate a polynomial function.

› Graph a polynomial function.

Section 6.1 Page 326 – 327 # 16 – 49 every 3, 50

is a function is in the form

f(x) = anxn + an-1xn-1 + an-2xn-2 + … + a1x1 + a0

All the coefficients are real numbers (not imaginary)

Exponents are whole numbers (positive integers) an is the leading coefficient n is the degree of the polynomial a0 is the constant term

0

1

2

3

4

Constant

Linear

Quadratic

Cubic

Quartic

Is it a polynomial? Is the polynomial in standard form? What is the degree of the polynomial What is the leading coefficient of the polynomial? What is the constant(y-intercept) of the polynomial?

a. f(x) = 3x2 + 3x3 – 4x5 + x – 6

b. f(x) = 4x3 – 14x -2 + x – 6

Examples:1. f(x) = 3x5 – x4 – 5x + 10 Find f(–2)

2. f(x) = –3x3 + 4x2 + 2x Find f(–3)

a) f(x) = 3x5 – x4 – 5x + 10, find f(–2)

–2 3 –1 0 0 –5 10

3

-6

-7

14

14

-28

-28

56

51

-102

-92

+

Step 1: Write the polynomial in standard form, if not already.Step 2: Write the coefficients of x as shown below and use synthetic substitution.

b) f(x) = –3x3 + 4x2 + 2x, find f(4)

Degree Leading Coefficient

Left-hand Behavior

Right-hand Behavior Picture

Even Positive

Even Negative

Odd Positive

Odd Negative

a) f(x) = -x3

What is the degree?

What is the leading coefficient?

Describe the end behavior

3 (odd)

-1 (negative)

Up on left, Down on right

Make a table and graph.

xfx

xfx

, as and

, As

x –2 –1 0 1 2

y

b) f(x) = x4 – 2x – 3

What is the degree?

What is the leading coefficient?

Describe the end behavior.

4 (even)

1 (positive)

Up on left, Up on right

Make a table and graph.

xfx

xfx

, as and

, As

x –2 –1 0 1 2

y

Section 6.2Page 333 - 335 #16 – 46 every 3, 49 – 52 all, 53 – 71 every 3