3.4e.1
Exercises - Polynomial Graphs
A: Concepts
1) What is the difference between an -intercept and a zero of a polynomial function ?
2) If a polynomial function of degree has distinct zeros, what do you know about the graph of the function?
3) What is the relationship between the degree of a polynomial function and the maximum number of turning points in its
graph? .
4) Explain how the factored form of the polynomial helps us in graphing it.
5) If the graph of a polynomial just touches the -axis and then changes direction, what can we conclude about the factored
form of the polynomial?
Answers to odd exercises:
1. The -intercept is where the graph of the function crosses the -axis, and the zero of the function is the input value for
which .
3. The maximum number of turning points is one less than the degree of the polynomial.
5. There will be a factor raised to an even power.
B: Multiplicity from an Equation
Find the zeros and give the multiplicity of each.
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
Answers to odd exercises:
7. and with multiplicity , with multiplicity
9. with multiplicity , with multiplicity
11. with multiplicity , with multiplicity
13. with multiplicity , and with multiplicity
15. with multiplicity , with multiplicity
17. with multiplicity , with multiplicity
C: Multiplicity from a Graph
Use the graph to identify zeros and multiplicity.
Exercise
3.4
e
.
A
x f
n n
x
x x
f
(
x
) = 0
Exercise
3.4
e
.
B
★
f
(
x
) = (
x
+ 2 (
x
− 3)3)2
f
(
x
) = (2
x
+ 3 (
x
− 4
x
2)5)2
f
(
x
) = (
x
− 1 (
x
+ 2)
x
3)3
f
(
x
) = ( +4
x
+ 4)
x
2
x
2
f
(
x
) = (2
x
+ 1 (9 −6
x
+ 1))3
x
2
f
(
x
) = (3
x
+ 2 ( − 10
x
+ 25))5
x
2
f
(
x
) =
x
(4 − 12
x
+ 9)( + 8
x
+ 16)
x
2
x
2
f
(
x
) = − − 2
x
6
x
5
x
4
f
(
x
) = 3 + 6 + 3
x
4
x
3
x
2
f
(
x
) = 4 − 12 + 9
x
5
x
4
x
3
f
(
x
) = 2 ( − 4 + 4
x
)
x
4
x
3
x
2
f
(
x
) = 4 (9 − 12 + 4 )
x
4
x
4
x
3
x
2
0 4 2 − 3
25
0 2 −2 2
−2
35 5 2
0 4 2 −1 1
3
22 0 3
0 6 2
32
Exercise
3.4
e
.
C
★
