Practice Page
Directions: Answer these questions pertaining to the graphs of polynomial functions. Choose the best answer. The cartoon "comments" may, or may not, be helpful!

1.
Given: P(x) = x2 + 2x - 24
At what x-values will the graph cross the x-axis?
graphfaccartoon1
       Choose:
 
x = +6, x = -4
x = +3, x = -8
  x = +4, x = -6 x = -3, x = 8

 

 

2.
A polynomial function is defined to be
f (x) = (x + 3)(x - 2)2.
Which choice describes the graph's behavior at the x-axis?
grapolycartoon2
Choose:
The graph only touches the x-axis at x = -3, but crosses the x-axis at x = 2.
The graph only touches the x-axis at x = 3, but crosses the x-axis at x = -2.
The graph only touches the x-axis at x = 2, but crosses the x-axis at x = -3.
The graph only touches the x-axis at x = -2, but crosses the x-axis at x = 3.

 

 

3.
Given:  the graph at the right.
Which choice lists possible "factors" of this polynomial function?
prac3graph
Choose:
(x - 4)(x - 1)(x + 1)
x = -4; x = -1; x = 1
x = 4; x = 1; x = -1
(x + 4)(x + 1)(x - 1)

 

 

4.
Given: the graph at the right.
Which polynomial function may represent this graph?
Choose:
prac4graph
P(x) = -(x - 1)(x + 1)(x + 2)
  P(x) = -(x + 1)(x - 2)
  P(x) = -(x + 1)2(x - 2)
  P(x) = -(x - 1)2(x + 2)

 

 

5.
Given: the graph at the right.
Which choice lists possible "roots" of this polynomial function?
Choose:
(4x + 3)(x - 1)(8x - 23)
x = -3/4; x = 1; x = 23/8
x = -3/4; x = 1; x = 7/8
(4x - 3)(x + 1)(8x + 7)
prac5graph

 

 

6.
Given: P(x) = x3 + 6x2 + 8x
Which choice shows the roots of this polynomial function?
Choose:
x = 0, -2, -4
 x = 0, 2, -4
x = 0, 2, 4 x = 0, -2, 4
graphpolycartoon3

 

 

7.
Given: P(x) = x2 - 2x - 48
Which choice shows the x-intercepts of this polynomial function?
graphpolycartoon5
Choose:
(-8,0), (6,0)
(-6,0), (8,0)
(0,-8), (0,6)
(0,-6), (0,8)

 

 

8.
Given: P(x) = x2 - 6x + 9
Which choice states the number of x-intercepts of this polynomial function?
graphpolycartoon4a
       Choose:
 
1
2
3 0

 

 

9.
Based upon the sketch at the right, which expression may have been used to create P(x)?

sketch
Choose:
(x - 3)(x + 1)(x + 2)(x + 4)
(x - 3)(x + 2)(x + 4)
(x - 4)(x - 2)(x - 1)(x + 3)
(x - 4)(x - 2)(x + 3)

 

 

10.
By examining the roots of the graph at the right, write a possible equation, P(x), that could produce this graph.
Choose:
P(x) = x(x + 1)2
P(x) = x(x - 1)2
P(x) = x(x2 - 1)
P(x) = x(x2 + 1)




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