Name: ________________________________________
Date: ______________
Quadratics Review Sheet
Simplify completely.
1. √50
2. √270𝑥 20 𝑦 9
4. √108
5. 2√8 • 3√20
3
3. √3 • √6
48𝑥 6
6. √
64
Solve each equation. Be sure to give a complete answer in simplest radical form when
necessary.
7. 4x2 = 16
8. (x – 5)2 = 81
Find the roots using the square root method. No decimal answers! All non-perfect square
answers must be written as fully simplified square roots!
9. y = x2 – 25
10. f(x) = 3x2 + 48
Find the roots by factoring.
11. 2x2 – 5x = 3
12. y = x3 + 9x2 + 20x
13. (2x + 1)(x – 7) = 0
14. 4x(3x – 2)(x + 5) = 0
Find the roots using the quadratic formula.
15. 2x2 – x = 2
𝑥=
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
16. y = -x2 + 2x + 3
Quadratic formula continued…
𝑥=
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
17. y = 3x2 + 5x + 3
18. f(x) = 2x2 + 4x - 1
19. All quadratic functions will have either 0, 1, or 2 roots. Determine the discriminant then
use the discriminant to identify the number of roots for each function listed below.
Example
Discriminant
Number of Roots
y = 2x2 – 7x + 1
y = 4x2 – 4x + 1
y = 2x2 + 3
20. What are the real roots of 6x2 – 96 = 0?
A. 6, -4, and 4
B. 6 only
C. 4 and -4
D. 16 and 6
21. Draw a graph that has solutions
at -3 and 4.
22. For each example, determine the best method for finding the roots. Then,
explain why it is the best method.
A. y = 4x2 – 48
Best Method:
Reason:
B. y = x2 – 7x + 10
Best Method:
Reason:
C. y = 2x2 + 4x – 1
Best Method:
Reason:
D.
Best Method:
Reason: