12.4 Quadratic Formula
Name _____________________________
Learning Objective: A.REI.4 I will solve a quadratic equation by the quadratic formula
A.REI.4
I will find the discriminant of a quadratic equation
A.REI.4
I will use the discriminant of a quadratic equation to determine the number & type of solutions
A.REI.4
I will recognize when the quadratic formula gives a complex solution
Solve each equation below using the quadratic formula. Cross out the box that contains the solution
set. When you finish, print the letters from the remaining boxes in the spaces at the bottom of the page.
1. x2 + 4x + 3 = 0
2. x2 – 7x + 10 = 0
3. x2 + 5x + 6 = 0
4. x2 – 3x – 4 = 0
5. y2 + 2y – 8 = 0
6. 4x2 – 3x = 1
7. 2x2 + x – 6 = 0
8. 2x2 – 5x + 2 = 0
9. 2n2 – 3n – 5 = 0
10. 2x2 – 7x + 5 = 0
11. 3y2 – 2y – 8 = 0
Solve each using the quadratic formula. Give exact answers only.
12. x2 + 8x + 16 = 0
13. x2 – 5x – 10 = 0
14. x2 + 6x + 10 = 0
15. 10x2 – 5x – 25 = 0
16. 5x2 – x + 4 = 0
17. 3x2 – 2x – 9 = 0
Factor each expression completely.
18. 25x2 + 80x + 64
19. 16x2 – 81
Answers: 1) x = –1 , x = –3 or {–1, –3}
9) x 
5
, x  1
2
17) x 
11) x  
3) x = –3, x = –2
4
,x2
3
24 7
1 2 7
= x
3
6
20. x2 – 11x – 60
13) x 
5  65
2
19) (4x + 9)(4x – 9)
21. x2 + 3x – 40
5) x = 2, x = –4
15) x 
7) x 
3
, x  2
2
5  5 41
1  41
= x
20
4
21) (x + 8)(x – 5)