Name
savvasrealize.com
3-5 Additional Practice
Zeros of Polynomial Functions
Sketch the graph of the function by finding the zeros. List the zeros.
1. f(x) = 2 x 3 − 12 x 2 − 6x 2. f(x) = x 3 − 2 x 2 − 4x − 6
Find the zeros of each function and describe the behavior of the graph of the
function at each zero.
3. x 3−8x 2 + 18x 4. x 3 + x 2 − 3x + 1
Determine all the real and complex zeros of each polynomial function.
5. f(x) = x 3 − 7 x 2 + 4x − 28 6. f(x) = x 3 − x 2 − 2x + 8
7. A company that sells toys models their profit with the function
P(x) = −4 x 3 + 32 x 2 − 64. Their profit P, in thousands of dollars,
is a function of the number of toys sold x measured in hundreds.
What do the key features of the graph reveal about the profits?
What is the maximum profit the company can make?
Solve each inequality.
8. x 3 − 27x < 0 9. x 3 + 9 x 2 − 10x > 0
10. Useyourgraphingcalculatortodetermineiff(x) = (x − 1)(x −6)(x + 3)
is the correct factorization of f(x) = x 3 + 7 x 2 + 4x−12.Explain.
y
−40
−80
Ox
4 8
−4
y
10
O
x
−10
2 4
−2
x = 0, x = 3 ± 2
√
__
3 x = 3.6, x = −0.8 ± 1.02i
the graph crosses the
x-axis at 0
x = 7, 2i, −2i, x = −2, 3±i
√
__
7
______
2
the graph crosses the x-axis
at 1, 0.4, −2.4
x = 0, 3, 6
x = 1, −1 +
√
__
2 , −1 −
√
__
2
x < 3
The zeroes for f(x) = x 3 + 7 x 2 + 4x− 12 are x = −6, −2, 1, so
the correct factorization of the equation is (x+ 6)(x+ 2)(x+ 1).
The domain > 0; zeros: 1.58, 7.73; To earn a profit, the
company should make between 1,580 and 7,730 toys.
The maximum profit the company can make is $29,338.
x < 0; x > 1
enVision™ Algebra 2 • Teaching Resources
