Download Algebra 2

Algebra 2
Unit 5 Test Review
Name:___________________ Pd:____
**You may use a calculator on the ENTIRE Review and Test!
Simplify the following radical expressions.
1.
20
2.
4.
18
5. 24
3. 49
148
6.
16
Solve using SQUARE ROOT/RADICALS METHOD. Be sure your solutions are in simplest form!
7. 7r2 – 10 = 25
8. 2(x - 4)2 – 24 = -48
Solve using COMPLETING THE SQUARE METHOD. Be sure your solutions are in simplest form!
9.
x² + 6x + 4 = 0
10.
2x² - 4x +14 = 0
Convert the following from standard form to VERTEX FORM using Completing the Square Method.
Then state the Vertex of the parabola.
11.
y = x2 - 8x + 17
12.
y = 2x2 + 24x + 25
Vertex Form:_________________________
Vertex Form:___________________________
Vertex Point:_____________
Vertex Point:_____________
Find the value of the discriminant “D”, and then tell how many solutions equation has and what type of
solutions (rational, irrational, or imaginary)
13. 2x2 – 8x + 9 = 0
14. –3x2 – x + 10 = 0
15. x2 – 2x + 1 = 0
D: ________________
D: ________________
D: ________________
How Many? ________
How Many? ________
How Many? ________
rational / irrational / imaginary
rational / irrational / imaginary
rational / irrational / imaginary
Solve the quadratic equations using the quadratic formula. Show all steps! Ensure answers are in both
simplified radical format and decimal format as appropriate. x 
b  b2  4ac
2a
16. 2x2 – 6x - 8 = 0
17. x2 – 4x = -8
18. –2x2 + 8x – 9 = 0
Solutions: ________________
Solutions: ________________
Solutions: ________________
Given the solutions to a quadratic equation and a point that is on the graph, write the equation in Standard
Format y = ax2 + bx + c
19.
3,8 and Point (7, 20)
Equation: ___________________________
20.
1, 2
Point (1, -8)
Equation: _____________________________
Given the Vertex Point and another point on the parabola, write the equation in vertex format:
21. Vertex: (-3, 5); Point (4, 8)
22. Vertex (2, -3); Point (-3, -6)
Equation: _______________________
Equation: _________________________
Given the following ordered pairs, write a quadratic equation using Quadratic Regression.
23. (0,2); (2,2); (3,9)
24. (1,6); (-2, 20); (-7 ,7)
Equation: ________________________
Equation: ___________________________
Review:
25. A kicked football can be modeled by the function Y = -.076x2 + 4x + 1 where x is the distance
in meters down the field and y is the height (in meters) of the ball.
a) What is the maximum height of the kicked ball? _______________
b) What is the height of the ball when kicked? _________________
c) How far does the ball go down field? _______________________
Factor the following and then find the solutions from the factors:
26. 49 x 2  9  0
27. x 2  2 x  8  0
28. 12 x 2  x  1  0
Factors: _______________
Factors: _________________
Factors: _________________
Solutions: _____________
Solutions: _______________
Solutions: ________________
Thought Question:
We have learned 5 methods to find the solutions to a quadratic equation. List the 5 methods below and
discuss the limitations (what type problem won’t the method solve?)
Method
Name
Limitations