Show:
Quadratic Functions
Polynomial Functions and Their Graphs
Dividing Polynomials, Remainder and Factor Theorems
Rational Functions and Their Graphs
100

What is the Vertex?

f(x)= -3(x+3)2-11

(-3,-11)

100

If it is 'Even Negative' which direction do the arrows point?

Down, Down

100

x7+x5-10x3+12/x-2

Use Synthetic Division to state the

Q(x):

R(x):  

Q(x): x6+2x5+5x4+10x3+10x2+20x+40

R(x): 92

100

What is the Horizontal Asymptote of:
f(x)= 15x2/-3x2+1

HA: -5

200

What is the Vertex?

f(x)= -3x2+12x+5

(2,17)

200

If it is 'Odd Positive' which direction do the arrows point?

If it is 'Odd Negative' which direction do the arrows point?

Down, Up

Up, Down

200

5x3+6x+8 by x+2

Use Synthetic Division to state the

Q(x):

R(x):  

Q(x): 5x2-10x+26

R(x): -44

200

What is the Horizontal Asymptote of:
f(x)= -3x-7/5x2-2

HA: 0

300

Write the equation of the parabola in standard form

Vertex: (2,-4)

Passes through point (-5,1)

f(x)=5/49(x-2)2-4

300

What is the End Behavior of:

f(x)=x3+3x2-4x-12

End Behavior:

Odd, Positive

Down, Up

300

Use Synthetic Division and the Remainder Theorem

f(x)=x3-7x2+5x-6 ; f(-6)

Is there a factor?

x2-13x+83-504/x+6

Q(x): x2-13x+83

R(x): -504

There is no factor, because using the Remainder Theorem the remainder should have been a zero in order for x+6 to be a factor 


300

f(x)= 3x/x-1

Find x-int:

Find y-int:

How did you figure it out?

x-int: x=0

y-int: y=0

400

f(x)= (x+2)2-4

Find:
Vertex?

Axis of Symmetry?

X-int?

Y-int?

Vertex: (-2,-4)

Axis of Symmetry: x=-2

X-int: x=0 and x=-4

Y-int: y=0

400

f(x)= x3+x2-4x-4

Find Zeros and Multiplicity:

What is the End Behavior:

State the Symmetry:

x=-2 M=1

x=2 M=1

x=-1 M=1

End Behavior: Down, Up

State the Symmetry: The polynomial contains both even and odd exponents so it cannot have symmetry

400

Use Synthetic Division and the Remainder Theorem

f(x)=2x6+10x3+8 divided by x+1 ; f(-1)

Is there a factor?

2x5-2x4+2x3+8x2-8x+8

Q(x): 2x5-2x4+2x3+8x2-8x+8

R(x):0

f(-1)= 2(-1)6+10(-1)3+8

f(-1)= 2-10+8 = 0

The remainder is 0 so x+1 is a factor of this polynomial


400

f(x)= x-4/x2-x-6

Find x-int:

Find y-int:

How did you figure it out?

x-int: x=4

y-int: y=2/3

500

f(x)= 5-4x-x2

Find:
Vertex?

Axis of Symmetry?

X-int?

Y-int?

Vertex: (-2,9)

Axis of Symmetry: x=-2

X-int: x=-5 and x=1

Y-int: y=5

500

f(x)= -x2(x+2)(x-2)

Find Zeros and Multiplicity:

What is the End Behavior:

State the Symmetry:

x=0 M=2

x=-2 M=1

x=2 M=1

End Behavior: Down, Down

State the Symmetry: Even, with respect to the y-axis. This means that the graph is a mirror image across the y-axis

500

Long Division
120x-12000 divided by x-160

120+7200/x-160

500

h(x)= x+6/6x2-11x-10

Find the Vertical Asymptote

VA: -2/3 and 5/2