Cc-26 Polynomial Functions Examples And Worksheet - Common Core Page 7
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8B
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40.
Think About a Plan
The data shows the power generated by a wind turbine. The
x
y
x column gives the wind speed in meters per second. The y column gives the
power generated in kilowatts. What is the degree of the polynomial function
5
10
that models the data?
6
17.28
• What are the first differences of the y-values?
7
27.44
• What are the second differences of the y-values?
8
40.96
• When are the differences constant?
9
58.32
Classify each polynomial by degree and by number of terms. Simplify first if
necessary.
1
2
1
2
1
2
2
3
4
+ a
- 4a
41. a
42. 7
43. 2x(3x)
2
3
3
2
44. (2a - 5)
- 1
45.
-8d
- 7
+
-d
- 6
46. b(b - 3)
a
Determine the sign of the leading coefficient and the least possible degree of
the polynomial function for each graph.
y
y
y
47.
48.
49.
2
2
2
x
x
x
2
2
2
2
2
2
2
2
50.
Open-Ended
Write an equation for a polynomial function that has three
turning points and end behavior up and up.
51. Show that the third differences of a polynomial function of degree 3 are nonzero
3
2
and constant. First, use f (x) = x
- 3x
- 2x - 6. Then show third differences are
3
2
nonzero and constant for f (x) = ax
+ bx
+ cx + d, a
0.
52.
Reasoning
Suppose that a function pairs elements from set A with elements
from set B. A function is called onto if it pairs every element in B with at least one
element in A. For each type of polynomial function, and for each set B, determine
whether the function is always, sometimes, or never onto.
a. linear; B = all real numbers
b. quadratic; B = all real numbers
c. quadratic; B = all real numbers greater than or equal to 4
d. cubic; B = all real numbers
53. Make a table of second differences for each polynomial function. Using your tables,
make a conjecture about the second differences of quadratic functions.
2
2
2
a. y = 2x
b. y = 5x
c. y = 5x
- 2
2
2
2
d. y = 7x
e. y = 7x
+ 1
f. y = 7x
+ 3x + 1
54. a. Write the equation for the volume of a box with a length that is 5 in. less than its
width and a height that is 3 in. less than its width.
b. Graph the equation.
c. For which interval(s) does the graph increase?
d. For which interval(s) does the graph decrease?
124
Honors Supplement
124
Common Core
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