Algebra II
Web Quiz 7.1 -7.4
Answers
Name:____________________________________________________
Find f  2 for each function .
1). f x   x  2
2).
f  2  2  2  4
f x   x 2  5 x  2
f  2   2  5 2  2
f  2  16
2
Find g x  2 for each function
g x  
3). g x   x  2 x  1
4).
g x  2  x  2  2x  2  1
g x  2 
2
2
g  x  2  x 2  4 x  4  2 x  4  1
g  x  2  x 2  6 x  7
1
x 1
2
1
x  2  1
2
1
g  x  2  x  1  1
2
1
g x  2  x
2
For each graph,
a). describe the end behavior
b). determine whether it represents an odd-degree or an even-degree polynomial function
c). state the number of real zeros.
5).
6).
a). x   f x    , x  
x   f x   
f x   
a). x   f x    ,
b). odd degree polynomial
b). even degree polynomial
c). one real zero
c). four real zeros
For questions, 7 and 8 state the following
a). graph each function by making a table of values
b). determine consecutive values of x between which each real zero is located
c). estimate the x-coordinates at which the relative maxima and relative minima occur
7).
f x   x 3  3x 2  36 x  32
a). graph in viewing window [-10,10] by [-20,200]
[-10,10] by [-25,10]
TABLE:
2
8). f x   x  10 x  9
a). graph in viewing window
TABLE:
b). real zeros at x = -8, 1, 4
between 9 and 10
b). real zeros at x = 1 and
c). Max at x = -4.605
Min at x = 2.605
c). min at x = 4.999
9). Sketch a graph of a polynomial , that has 4 roots and is even.
10). Sketch a graph of each polynomial that is odd and has three roots.
Solve the following the equations.
4
2
11). x  13x  36  0
x2  4 x2  9  0
x  2x  2x  3x  3  0



3
12). x  343  0
x  7 x 2  7 x  49  0
x  7  0 and


x 2  7 x  49  0
and x  7  7i 3
2
x  2,2,3,3
x = -7
13). x  4 x  12  0
14). x 3  8 x 3  15  0
2
1

x 6



x 6  0 x 2  0
 13
 1

 x  5  x 3  3  0






1
 3

 x  5   0 and




x 2 0
 

 13

 x  3  0




1
x  6 and x  2
x = 36 and not possible
1
x 3  5 and x 3  3
x = 125 and x =27
Use Synthetic Substitution to find f 3 for each function.
3
2
15). f x   x  2 x  7 x  1
4
2
16). f x   x  4 x  2 x  10
3| 1
3| 1
2 7 1
3 15 66
1 5 22 67
f 3  67
1
0 4 2 -10
3 9 39 123
3 13 41 113
f 3  113
Given the polynomial and one of its factors, find the other factors of the polynomial.
3
2
17). x  6 x  x  30
Factor is x  3
-3 | 1
6
-3
1 3
-1
-30
-9
30
-10
0
Depressed polynomial is: x 2  3x  10
x 2  7x  6
3
2
18). x  4 x  15x  18
Factor is x  3
3|
1
1
4
3
7
-15
21
6
-18
18
0
Depressed polynomial is:
Factor polynomial:
x  1x  6
x  2x  5
Factor Polynomial:
5
4
3
2
19). Use the graph that you create from the equation: y  x  x  3x  3x  4 x  4 , to
determine at least one binomial factor of the polynomial. Then find all the factors of the
polynomial.
Possible factors are: x + 2, x + 1, x – 2
Prove that they are factors
-2 | 1
-1|
1
2|
1
1
1 -3 -3
-4
-4
-2 2 2
2
4
-1 -1 -1 -2
0
-1 2 -1
2
-2
1 -2
0
2
0
2
0
1
0
Depressed polynomial is x 2  1
5
4
3
2
The factors for the equation: y  x  x  3x  3x  4 x  4 are
x 2  1 x  2x  1x  2

