End Behaviors & Degree
What's the value of a?
Polynomial zeros
Write the equation
Zeros & Multiplicity
100
What is the degree and end behavior?
f(x) = -x^4 + x^2 -x -3
4 (quartic)
Both ends down
100
The function
y = a(x-2)(x+3)
through the point (1, -16).
a = 4
100
Find the zeros of the function: y = (x - 3)(x + 2)
x = -2 or 3
100
Decide if the value of a is + 1 or -1
y=(x+4)(x+1)(x-1)(x-3)
100
Find the zero(s) and the multiplicity for each zero
f(x)= x^2 - 4
x = 2 and -2, both multiplicity of 1
200
What is the degree and end behavior?
f(x)=-5x^5+3x^3-3x+1
5 (quintic)
Up on left and down on right
200
The function
g(x) = a(x-4)(x+2)(x-1)
through the point (2, -16).
a = 2
200
Which special points on graphs will help you to find its zeros?
The x-intercepts
200
Decide if the value of a is + 1 or -1
-(x+3)^2(x-5)
200
Find the zero(s) and the multiplicity for each zero
f(x) = x^2 + 10x + 25
zero:x=-5 multiplicity of 2
300
What is the end behavior and degree of the function?
f(x)=(x-3)(x+6)(x-8)^2
4 - Quartic
Both ends up
300
The function
y=a(x-3)^2(x+2)
through the point (2, -8).
a = -2
300
Find the zeros of the function: y = x(x + 1)(x - 7)
x = 0, -1 and 7
300
Decide if the value of a is + 1 or -1
(x+4)(x+2)(x-3)^2
300
x = -3 (multiplicity 1)
x = 2 (multiplicity 2)
x = 5 (multiplicity 1)
400
What is the end behavior and degree of the function?
f(x) = (x-3)^2(x+4)(x-1)^2
5 - Quintic
Down on left and up on right
400
The function
g(x)=a(x-5)^2(x+2)^2
through the point (4, 18).
a = 0.5
400
Find the zeros for y = x3 + 2x2 - x - 2
x = 1, -1, -2
400
Decide if the value of a is + 1 or -1
g(x)= -x(x+2)(x-2)^2
400
x = -1 (multiplicity 2)
x = 2 (multiplicity 3)
x = 4 (multiplicity 1)
500
What is the degree and the end behaviors of the function?
f(x) = -2x(x+3)(x-8)^2
4 - quartic
Both ends down
500
The function
y = a(x+3)^2(x-2)^2(x+5)
through the point (-2, -24).
a = -0.5
500
Solve 
X = -1 and x = 5 (double root)
500
Write a polynomial equation for a graph that passes through the point (1, 56) and has three x-intercepts: (–3, 0), (2, 0), and (5, 0).
y = 3.5(x + 3)(x − 2)(x − 5)
500
Find a polynomial function leading coefficient of -2 and with given zeros and multiplicity : zero: -5, multi: 3 | zero:0 , multi:2
y = -2x^2(x+5)^3