Quadratic Formula Review
Geometry 830
1. State the quadratic formula.
2. Which part of this formula represents the discriminant?
3. What does it indicate?
4. On a graph, what would the answer to #3 mean?
Identify a, b, and c for the following quadratics.
5. 3x2 + 5x = 2
6. y2 = 7y – 4
8. 6 – 3x2 = 0
9.
2 2
x + 4x + 5 = 0
3
7. 2w2 = 5
10. 3f2 + 4 = 2f
Find the value of the discriminant and determine the number of roots for the
quadratic. Indicate whether the root is rational, real, or imaginary.
11. x2 + 4x – 4 = 0
12. 2n2 – 5n – 1 = 0
13. 3x2 – 6x + 30 = 0
14. x2 – 4x + 5 = 0
15. y2 = 4y – 1
15. 4x2 + 12x = -9
16, 16x2 + 1 = 8x
17. 2n2 = 5n – 3
18. 5u2 + 6u + 2 =0
19. 6x2 – 4x = -1
20. 15 – 3y2 = 0
21. 6x + 2 = -5x2
Solve using the quadratic formula. Leave irrational roots in simplest radical form.
22. x2 +
5
3
x =0
2
2
24. x(2x -1) – 3(x + 4) = 0
23. 4x (x – 2) = 5(x – 1)
25. x 2  3  x 6
26. x 2  2 x 5  3
27. 2(x + 3)2 = 5(x + 2)2
28. (y + 1)2 – 2(y – 2)2 = 8
29. a2 + 6a + 7 = 0
30. 5a2 + 7a = 6
31. 2y2 – 8y + 3 = 0
32. 6x2 – 4 = 5x
33. x 2 
2
4
x 0
3
3
Solve the following quadratics using the quadratic formula and give the answers
to the nearest hundredth.
34. 8x2 – 2x = -1
35. 2x2 + 8x = -5
36. y2 + 6y + 4 = 0
37. x2 = -3x + 4
Quadratic Formula Review
Answers
1.
 b  b 2  4ac
x
2a
2. b 2  4ac
25. x 
6 3 2
2
26. x 
2 54 2
2
27. x 
 4  10
3
3. The number of real solutions
4. The number of places the
function touches the x-axis
5. a = 3, b = 5, c = -2
28. x  5  10
6. a = 1, b = -7, c = 4
29. x  3  2
7. a = 2, b = 0, c = -5
3
30. x  ,  2
5
8. a = -3, b = 0, c = 6
9. a = 2, b = 12, c = 15
10. a = 3, b = -2, c = 4
11. 2 real roots
31. x  2 
32. x 
4
1
,
3
2
33. x 
 1  13
3
12. 2 real roots
13. 2 imaginary roots
14. 2 imaginary roots
10
2
15. 2 real roots
34. No Real Roots
15. 1 rational root
35. x = -0.78, -3.22
16. 1 rational root
36. x = -0.76, -5.24
17. 2 rational roots
37. x = 1, -4
18. 2 imaginary roots
19. 2 imaginary roots
20. 2 real roots
21. 2 imaginary roots
22. x = ½, -3
23. x 
13  89
8
24. x  1  7