Name: ________________________ Class: ___________________ Date: __________
ID: A
Test # 3 Review
Short Answer
1. Find the standard form of the quadratic function shown below:
2
2. Compare the graph of m (x )  9 (x  7 ) 2  5 with m (x )  x .
ÍÈÍ 1
˙˘˙ 2
3. Compare the graph of n  ÍÍÍÍ  (x  4 ) ˙˙˙˙  8 with n (x )  x .
˙˚
ÍÎ 3
2
4. From the graph of the quadratic function f (x )  (x  2 ) 2  9, determine the equation of the axis of
symmetry.
2
5. Determine the x-intercept(s) of the quadratic function f (x )  x  10x  26.
2
6. Determine the x-intercept(s) of the quadratic function f (x )  x  4x  32.
2
7. Determine the vertex of the graph of the quadratic function f (x )  x  x 
2
5
.
4
8. From the graph of the quadratic function f (x )   x  8x  5, determine the equation of the axis of
symmetry.
2
9. Write the quadratic function f (x )  x  4x  3 in standard form.
2
10. Write the quadratic function f (x )   x  2x  2 in standard form.
1
Name: ________________________
11. Write the quadratic function f (x ) 
ID: A
1
8
ÊÁ 2
ˆ
ÁÁÁ x  16x  8 ˜˜˜˜ in standard form.
Ë
¯
12. Write the standard form of the equation of the parabola that has a vertex at (8,  3) and passes
through the point (6, 2).
13. Write the standard form of the equation of the parabola that has a vertex at
ÊÁ 2 1 ˆ˜
ÁÁ
, ˜˜˜˜ and passes
ÁÁ
9¯
3
Ë
through the point (1, 2).
14. Find two positive real numbers whose product is a maximum and whose sum is 156.
15. A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs.
The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.
3
2
4
3
16. Find all real zeros of the polynomial f (x )  x  6x  9x  54 and determine the multiplicity of
each.
2
17. Find all real zeros of the polynomial f (x )  x  5x  6x and determine the multiplicity of each.
4
2
18. Find all real zeros of the polynomial f (x )  x  52x  576 and determine the multiplicity of each.
3
19. Using a graphing utility, graph f (x )  x  4x and approximate the zeros and their multiplicity.
20. Use long division to divide.
ÊÁ 3
ˆ
ÁÁ x  5x 2  16x  80 ˜˜˜  (x  5 )
ÁË
˜¯
21. Use long division to divide.
ÊÁ 3
ˆ
ÁÁ x  8 ˜˜˜  (x  2 )
ÁË
˜¯
2
Name: ________________________
ID: A
22. Use synthetic division to divide.
ÁÊÁ 4x 3  x 2  11x  6 ˜ˆ˜  (x  2 )
ÁÁ
˜˜
¯
Ë
23. Use synthetic division to divide.
ÊÁ
ˆ
ÁÁ 24  5x 3  22x  27x 2 ˜˜˜  (x  2 )
ÁË
˜¯
24. Use synthetic division to divide.
ÊÁ 3
ˆ
ÁÁ x  27x  54 ˜˜˜  (x  3 )
ÁË
˜¯
3
2
25. Write f (x )  x  3x  3x  32 in the form f (x )  (x  k )q (x )  r when k  5.
2
26. If f (x )   3x  4x  1, use synthetic division to evaluate f (4) .
3
2
27. If x   1 is a root of x  4x  x  4  0 , use synthetic division to factor the polynomial
completely and list all real solutions of the equation.
3
28. If x 
2
7 is a root of x  3x  7x  21  0 , use synthetic division to factor the polynomial
completely and list all real solutions of the equation.
3
2
29. Using the factors (x  5 ) and (x  2 ), find the remaining factor(s) of f (x )  x  6x  3x  10 and
write the polynomial in fully factored form.
30. Using the factors (3x  2) and (x  1 ), find the remaining factor(s) of
4
3
2
f (x )   6x  23x  12x  11x  6 and write the polynomial in fully factored form.
3
31. Simplify the rational expression,
2
3x  x  40x  48
, by using long division or synthetic division.
3x  4
Ê
Ë
ˆ
¯
32. Find all zeros of the function f (x )  x (x  2 ) ÁÁÁÁ x  216 ˜˜˜˜ .
2
3
33. Find all zeros of the function f (x )  (x  2 ) (x  3i ) (x  3i ) .
È
˘È
˘
34. Find all zeros of the function f (x )  (x  4 ) (x  3 ) ÍÍÍÎ x  (4  3i) ˙˙˙˚ ÍÍÍÎ x  (4  3i) ˙˙˙˚ .
5
4
3
2
35. Find all the rational zeros of the function f (x )  2x  3x  9x  3x  11x  6.
3
Name: ________________________
ID: A
3
2
36. Given 5i is a root, determine all other roots of f (x )  x  5x  25x  125.
5
4
3
2
37. Given 1  i is a root, determine all other roots of f (x )  x  8x  24x  32x  20x .
38. Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of
5
f (x )  x  2x .
39. Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of
3
2
f (x )  x  4x  6x  5.
3
2
40. Find all the real zeros of f (x )  6x  8x  6x  8.
4
ID: A
Test # 3 Review
Answer Section
SHORT ANSWER
1. ANS:
f (x )  3 (x  1 ) 2
PTS: 1
2. ANS:
REF: 78
OBJ: Determine the standard form of a quadratic function
m (x )  9 (x  7 ) 2  5 shifts right 7 units, shifts upward 5 units, and stretches by a factor of 9.
PTS: 1
3. ANS:
REF: 67
OBJ: Compare transformed graph to base graph
PTS: 1
4. ANS:
REF: 68
OBJ: Compare transformed graph to base graph
PTS: 1
5. ANS:
REF: 71
OBJ: Determine axis of symmetry
PTS: 1
6. ANS:
REF: 73
OBJ: Determine x-intercepts of quadratic function
PTS: 1
7. ANS:
REF: 74
OBJ: Determine x-intercepts of quadratic function
PTS: 1
8. ANS:
REF: 70
OBJ: Determine vertex of quadratic function
PTS: 1
9. ANS:
REF: 72
OBJ: Determine axis of symmetry
REF: 76
OBJ: Write quadratic function in standard form
˘˙ 2
ÍÈÍ 1
˙
1
n (x )  ÍÍÍÍ  (x  4 ) ˙˙˙˙ – 8 shifts left 4 units, shifts downward 8 units, and shrinks by a factor of .
9
˙˚
ÍÎ 3
x  2
no x-intercept(s)
(4, 0) , (8, 0)
ÊÁ 1
ÁÁ
,
ÁÁ
Ë 2
ˆ˜
1 ˜˜˜
˜¯
x  4
f (x )  (x  2 ) 2  1
PTS: 1
1
ID: A
10. ANS:
f (x )   (x  1 ) 2  3
PTS: 1
11. ANS:
f (x ) 
REF: 75
1
(x  8 ) 2  7
8
PTS: 1
12. ANS:
f (x ) 
REF: 77
OBJ: Write quadratic function in standard form
5
(x  8 ) 2  3
4
PTS: 1
13. ANS:
f (x ) 
OBJ: Write quadratic function in standard form
REF: 79
17
25
PTS: 1
14. ANS:
OBJ: Write standard form of a parabola
2
ÁÊÁ
˜ˆ
ÁÁ x  2 ˜˜˜  1
Á
3 ˜¯
9
Ë
REF: 80
OBJ: Write standard form of a parabola
PTS: 1
15. ANS:
REF: 81
OBJ: Application: Quadratic functions
PTS: 1
16. ANS:
REF: 83
OBJ: Application: Quadratic functions
PTS: 1
17. ANS:
REF: 90
PTS: 1
18. ANS:
REF: 92
PTS: 1
19. ANS:
REF: 91
PTS: 1
20. ANS:
REF: 93
OBJ: Approximate roots with graphing utility
REF: 98
OBJ: Divide polynomials using long division
78, 78
42'  56'
x  3, multiplicity 1; x   3, multiplicity1; x  6, multiplicity 1
OBJ: Determine zeros and multiplicity
x  0, multiplicity 2; x   3, multiplicity 1; x   2, multiplicity 1
OBJ: Determine zeros and multiplicity
x  4,multiplicity 1; x  4, multiplicity 1; x  6,multiplicity 1; x  6,multiplicity 1
OBJ: Determine zeros and multiplicity
x  0, multiplicity 1; x  2, multiplicity 1; x   2, multiplicity 1
2
x  16
PTS: 1
2
ID: A
21. ANS:
2
x  2x  4
PTS: 1
22. ANS:
REF: 99
OBJ: Divide polynomials using long division
2
4x  7x  3
PTS: 1
REF: 102
OBJ: Divide polynomials using synthetic division of polynomial
23. ANS:
2
5x  17x  12
PTS: 1
REF: 103
OBJ: Divide polynomials using synthetic division of polynomial
24. ANS:
2
x  3x  18
PTS: 1
REF: 104
OBJ: Divide polynomials using synthetic division of polynomial
25. ANS:
Ê
ˆ
f (x )  (x  5 ) ÁÁÁÁ x 2  2x  7 ˜˜˜˜  3
Ë
¯
PTS: 1
26. ANS:
REF: 107
OBJ: Rewrite polynomial: quotient and remainder
PTS: 1
27. ANS:
REF: 109
OBJ: Evaluate using synthetic division
PTS: 1
28. ANS:
REF: 111
f (4)   63
(x  4 ) (x  1 ) (x  1 ) ; x   4,  1, 1
Ê
(x  3 ) ÁÁÁ x 
Ë
ˆÊ
7 ˜˜˜ ÁÁÁ x 
¯Ë
ˆ
7 ˜˜˜ ; 3,
¯
PTS: 1
29. ANS:
REF: 113
PTS: 1
30. ANS:
REF: 114
PTS: 1
REF: 115
OBJ: Factor using synthetic division
7, 
7
OBJ: Factor using synthetic division
f (x )  (x  5 ) (x  2 ) (x  1 )
OBJ: Factor polynomial given factor(s)
f (x )  (3x  2) (x  3) (2x  1) (x  1 )
OBJ: Factor polynomial given factor(s)
3
ID: A
31. ANS:
2
x  x  12
PTS: 1
32. ANS:
REF: 117
OBJ: Approximate roots with graphing utility
x  0,  2, 6,  3  3 3 i,  3  3 3 i
PTS: 1
33. ANS:
REF: 119
OBJ: Determine zeros of polynomial
PTS: 1
34. ANS:
REF: 120
OBJ: Determine zeros of polynomial
PTS: 1
35. ANS:
REF: 121
OBJ: Determine zeros of polynomial
PTS: 1
36. ANS:
REF: 123
OBJ: Determine zeros of polynomial
PTS: 1
37. ANS:
REF: 129
OBJ: Approximate zeros with graphing utility
PTS: 1
38. ANS:
REF: 131
OBJ: Determine zeros of polynomial
x   2,  3i, 3i
x  4,  3,  4  3i, 4  3i
x 
1
, 3, 2
2
x   5, 5i
x  3  i, 1  i, 0
no positive reals; no negative reals
PTS: 1
39. ANS:
REF: 135
OBJ: Apply Descartes' Rule of Signs
3 positive reals or 1 positive real; no negative reals
PTS: 1
40. ANS:
x  
REF: 136
OBJ: Apply Descartes' Rule of Signs
REF: 139
OBJ: Determine zeros of a function
4
3
PTS: 1
4