Quadratic Functions
What is the Vertex?
f(x)= -3(x+3)2-11
(-3,-11)
If it is 'Even Negative' which direction do the arrows point?
Down, Down
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
What is the Horizontal Asymptote of:
f(x)= 15x2/-3x2+1
HA: -5
What is the Vertex?
f(x)= -3x2+12x+5
(2,17)
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
5x3+6x+8 by x+2
Use Synthetic Division to state the
Q(x):
R(x):
Q(x): 5x2-10x+26
R(x): -44
What is the Horizontal Asymptote of:
f(x)= -3x-7/5x2-2
HA: 0
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
What is the End Behavior of:
f(x)=x3+3x2-4x-12
End Behavior:
Odd, Positive
Down, Up
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
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
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
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
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
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
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
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
Long Division
120x-12000 divided by x-160
120+7200/x-160
h(x)= x+6/6x2-11x-10
Find the Vertical Asymptote
VA: -2/3 and 5/2