A2_4.2.1 Video Lesson - Polynomials: Zeros and Multiplicity

Where the graph crosses the y-axis

The highest or lowest point of the graph

Where the graph crosses the x-axis

The slope of the graph

(x + c)

(x - c)

(c - x)

(x * c)

The graph bounces off the x-axis

The graph goes through the x-axis

The graph approaches infinity

The graph has a horizontal asymptote

The graph goes through the x-axis

The graph bounces off the x-axis

The graph becomes a straight line

The graph has a vertical asymptote

bounce(2)

root = 4

mult = 1

$$x^2$$  

f(x)

$$\left(x-1\right)^4$$  

bounce(1)

root = -5

root = 0

mult = 3

through(1)

mult = 4

mult = 2

root = 1

root = 3

$$\left(x+5\right)$$  

root = 2

through(2)

$$y=x(x-3)^2$$

$$y=x(x^2-6x+9)$$

$$y=x(x+3)^2$$

$$y=(x-3)^3$$

0 and 3

0 and -3

1 and 3

1 and -3

x = 0 has multiplicity 1,

x = 3 has multiplicity 2

x = 0 has multiplicity 2,

x = 3 has multiplicity 1

x = 0 has multiplicity 1,

x = 3 has multiplicity 1

x = 0 has multiplicity 3,

x = 3 has multiplicity 2

It goes through

the x-axis.

It bounces off

the x-axis.

It approaches an asymptote.

It is undefined.