Name________________________
Date ________
Algebra2 HW: Factoring!
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
REVIEW (NOT OPTIONAL) – Simplify all of these (1pt each)
I.
2. (3  5)(4  2 5)
1.  2 3 32
3.
7
32
7
2
4. (3  i )(4  2i )
5.
35
7
II. PRACTICE – ( ½ pt each) Factor the following completely.
1. x2 + 3x - 18
4. x2 + 17x + 30
2. 9x2 - 121
5.
9x2 + 100
3. x2 – x – 42
6. 3x2 – 24x
III. PRACTICE – (1 pt each) Factor the following completely.
7. 12x2 – 27
10. 2x2 + 6x + 4
8. x2 – z2
9. 4x2 + 36
11. -6x2 + 24
12. 3x2 + 9x + 6
______
25
IV. MORE PRACTICE – 2 pts each Factor the following completely.
13. 9x2y2 – 64x2y2
16.
3y2 + y - 2
19. 4x2 – 21x + 5
14.
x4 + 13x3 + 30x2
17. 2x2 + 11x + 12
20. 6x2 - 7x - 5
IV. REACH FOR THE STARS! – 3 pts each
Factor the following.
22.
2(a + 4b)2 – 50c2
23. 4x8 – 25y4
15.
14r2 + r - 4
18. 9x2 + 30x + 25
21.
3x2 - 8x + 4
Name________________________
Date ________
Algebra 2 HW: Solving Quadratic Equations
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
______
25
I. REVIEW (NOT OPTIONAL) – complete all of these (1 pt each)
1. Simplify 3 12  3
1
4
3. Simplify 3y 2  y 3
2. Simplify
4. Simplify
3
2 x2  4 x 2
x2 y3
( xy)2
5. Simplify 2 6  24
II. PRACTICE – Factor the following polynomials. (½ pt each)
1. 4x2 + 2
2. x2 - 16
3. x2 – x - 72
4. x4 - 16
5. 3x2 – 8x + 5
6. 10x2 + 3x - 1
III. PRACTICE – Use a graphing calculator to determine the REAL solution(s) to the
quadratic equations. Remember there may be 0,1, 0r 2 solutions. Sketch the graph. (½ pt each)
7. 4x2 + 2
8.
x2 - 16
9.
x2 – 14x + 49
10. 4x2 - 81
11. x2 + 8x +16
12. x2 + 1
III. MORE PRACTICE – Solve the quadratic equations using the square root method.
Show your work. (1 point each)
13. x2 + 3 = 0
14. (x – 3)2 = 16
15. 2(x + 2)2 = 8
IV. MORE PRACTICE – Solve the quadratic equations using factoring. Show your work.
(2 points each)
16. 5x2 + 20x = 0
17. 3x2 – 7x = 0
18. x2 + x = 12
19.
2x2 + 13x – 7 = 0
20.
x2 = 4x + 5
21.
x2 – 9x + 14 = 0
22.
3x2 + x – 2 = 0
23.
4x2 – 25 = 0
24.
3x2 + 11x = - 6
IV. REACH FOR THE STARS! – 2 pts each. Factor the following.
25. 32x – 4
26. (x – y)2 – z2
Name________________________
Date ________
Algebra 2 HW: The Quadratic Formula
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
______
25
I. REVIEW (NOT OPTIONAL) – complete all of these (1 pt each)
3
1.
3
2.
2
3
4. Solve
3 3
2
3
a. 3( x  2)2  9
3. Simplify a.
b. 3( x  2) 2   9
128
b.  128
c. 3( x  2)2  0
5. Explain the difference in equations in #4. How did this affect your solutions?
II. PRACTICE – Compute the discriminant and describe the solutions. (2 pt each)
1. 3x2 + 2x – 1 = 0
2.
5x2 - 4x + 1 = 3x + 4
a=
b=
c=
(b)2 – 4(a)(c) =
nature of solutions: _______________
3.
-2x2 + x + 4 = 0
nature of solutions: _______________
nature of solutions: _______________
4.
-3x2 – 2 = x2 + 3x
nature of solutions: _______________
Part III. MORE PRACTICE - Solve using the quadratic formula. (2pts)
5. x2 + 4x – 2 = 0
6. 2x2 - 5x – 2 = 0
7. 2x2 - 9x + 9 = 0
8.
-x2 + 1 = -5x2 + 4x
9. 10x2 + x = 2
10. -6x2 + 3x + 2 = 3
11. 4x2 – 3 = 0
12. 3x2 + 2x = 0
IV. REACH FOR THE STARS! (4 pts) – Write the quadratic equation that has the
following solutions (roots):
13. a. x = 2i and x = -2i
b. Where does the quadratic cross the x-axis?
Name________________________
Date ________
Algebra 2 HW: Completing the Square
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
I.
1.
______
25
REVIEW (NOT OPTIONAL) – complete all of these (1 pt each)
Factor completely 3x2 + 9x
3. Factor completely
5. Simplify
x2 + x - 56
2. Factor completely
121x 2  64 y 2
4. Factor completely
6x2 + 7x - 3
1800x 2 y 8 z 9
II. PRACTICE – Fill in the blank to make the quadratic a perfect square trinomial.
Then, factor it. (1 pt each)
6. x2 + 6x + _______
factored: _______________
7. x2 + 12x + _______
factored: _______________
8. x2 - 24x + _______
factored: _______________
9. x2 - 30x + _______
factored: _______________
10. x2 - 2x + _______
factored: _______________
11. x2 + 7x + _______
factored: _______________ ** This may have a fraction in it!
III.Practice. Vertex Form (2 points)
12. a. Rewrite in vertex form: y = x2 - 18x + 86
b. Identify the following: Vertex __________
Axis of Symmetry __________
III. MORE PRACTICE – Solve the following by completing the square. 3 pts each
REMEMBER: You are finding WHERE THE QUADRATIC CROSSES THE X-AXIS.
13. x2 + 4x = 10
14. x2 + 8x = -1
15. x2 + 6x - 3 = 0
16. x2 + 12x + 18 = 0
17. 2x2 + 16x + 12 = 0
18. 4x2 - 40x - 12 = 0
IV. REACH FOR THE STARS! – Solve by completing the square. 3 pts each
19. a. x2 - 18x + 86 = 0
20. a. x2 - 2x + 25 = 0
b. Where does the quadratic cross
the x-axis?
b. Where does the quadratic cross
the x-axis?
Name________________________
Date ________
Algebra 2 HW: Quiz Review HW
SECTION 1: FACTORING
Factor Completely!
1.
x2 – 7x + 6
2.
x2 – 100
3.
4x2 + 81
4.
25p2 – 16p
5.
m2 – 10m + 21
6.
y2 – 3y – 18
7.
x2 + 7x + 12
8.
4x2 + 20x – 24
9.
4x2 + 20x + 25
10.
16a2 – 49b2
11.
16x2 + 6x
12.
x2 – 2x + 1
13.
16a2 – 81
14.
3x2 + 3x – 36
15.
x2 – 8x + 16
16.
24z2 – 14z – 5
17.
3m2 – 7m + 2
18.
3x2 – 75
SECTION 2: SOLVING
Use the square root method.
1.
5x2 – 7 = 60
3.
5x2 + 9 = 134
2.
x2 + 16 = 0
4.
2(x+3)2 + 12 = 4
Factor and use the zero product property.
5.
(2x + 8) (x – 5) = 0
6.
7.
x2 + 6x = 0
8.
x2 – 2x + 1 = 0
6x2 + 11x = 10
Complete the Square.
9.
x2 – 4x – 12 = 0
11.
x2 + 6x = 23
Use the Quadratic Formula.
13. x2 + 5x – 6 = 0
15.
2x2 – x – 4 = 2
10.
x2 – 2x – 35 = 0
12.
4x2 – 8x = 40
14.
2x2 – 4x + 3 = 0
16.
10x2 + 9 = x
Name________________________
Date ________
Algebra 2 HW: Solving Systems of Equations with Quadratics
______
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
25
I. REVIEW (NOT OPTIONAL) – complete all of these (1 pt each)
(4 – i)(3 – i)
1.
(2 + i) - (5 - 4i)
2.
3
7
3  4i
4. Solve x2 + 6 = 4
5. Solve x2 - 6 = 4
II. PRACTICE – Solve each system by graphing. If there is a solution, name it. If
there are infinitely many solutions or no solution, say so. (2 pts each)
6.
y  ( x  4) 2  1
1
y  x 1  7
2
7.
Solution: ___________________
x y 4
y    x  5
2
Solution: ___________________
 y
 y







    


x





    









x





8.
1
x 1
2
9.
y  3 x  7  2
3x  4 y  24
y
y   x  4   10
2
Solution: ___________________
Solution: ___________________
 y
 y







    
10.

x






    









3x  y  3
2 x  y  3
11.
Solution: ___________________




Solution: ___________________
 y









x  2y  4
4x  2 y  6
 y
    
x

x





    









x





12. Which is the apparent solution set to the system of equations shown on the graph? (1 pt)
A. { (3, 9) (-1, 9) }
B. { (0, 3) (0, 5) }
C. { (-1, 9) (1, 1) }
D. { (-1, 9) }
I. MORE PRACTICE – Solve the following by substitution. Show your work and use
your graphing calculator to check. 3 pts each
1.
y = x2 + x + 3
y = –3x + 8
2. y = x2 – 3x – 1
y = x + 20
3. y = 2x2 – 10
y = 4x – 12
4. y = x2 + 6x – 9
y = 2x – 13
IV. REACH FOR THE STARS! –4 pts
Write a system of equations that includes at least one quadratic function that has no solution. Sketch
your system to verify that it has no solutions.
 y




    





x




