Graphs of Polynomial Functions, Graphing Polynomial Functions - End Behavior, Polynomial Graphs

same

Even degree graphs have the _____ end behavior

down

Negative leading coefficient graphs go ___ to the right.

opposite

Odd degree graphs have the ____ end behavior

Zeros

The solutions/x-intercepts on a graph

Cubic

Degree 3

f(x) = (x+1)(x-1)

-1, 1

standard form of a polynomial

terms are arranged from the largest exponent to the smallest exponent

degree of a polynomial

the greatest degree(exponent/power) of any term in the polynomial

f(x) = -(x+1)²

-1 multiplicity 2

f(x) = -(x+1)²(x-1)²

-1 multiplicity 2, 1 multiplicity 2

f(x) = -(x+1)(x-2)²

-1, 2 multiplicity 2

f(x) = x²(x+2)²

-2 multiplicity 2, 0 multiplicity 2

f(x) = -x²(x+2)(x-1)

-2, 0 multiplicity 2, 1

f(x) = x²(x+2)(x-2)

-2, 0 multiplicity 2, 2

f(x) = x(x+2)(x-1)²

-2, 0, 1 multiplicity 2

f(x) = -x²(x-2)

0 multiplicity 2, 2

f(x) = x²(x-3)

0 multiplicity 2, 3

f(x) = -x(x+1)²(x-2)

0, -1 multiplicity 2, 2

f(x) = -(x-1)²

1 multiplicity 2

monomial

1 term

binomial

2 terms

trinomial

3 terms

Down/Down

Describe the end behavior of the following equation.

Down/Up

Describe the end behavior of the following equation.

Up/Down

Describe the end behavior of the following equation.

Up/Up

Describe the end behavior of the following equation.

leading coefficient

coefficient of the first term when the polynomial is in standard form

up

Positive leading coefficient graphs go ___ to the right.

cross

What is the behavior of a multiplicity 1 zero?

bounce

What is the behavior of a multiplicity 2 zero?

two turns

What is the behavior of a multiplicity 3 zero?

Turning Points

Where the graph changes directions

Y-Intercept

Where the graph crosses the y-axis

quadratic

a polynomial with a degree of 2

constant

a polynomial with a degree of zero; for example, 5