1. Unit 6 Part 2 Test Review
Algebra 1

2. Problem 1 – Multiple Choice
Which of the following quadratic functions has the roots − and −2−2 2 ?
A) 𝑥 2 +4𝑥−4
B) 𝑥 2 +4𝑥+4
C) 𝑥 2 −4𝑥−4
D) 𝑥 2 −4𝑥+4

3. Problem 2 – Multiple Choice
Solve 3 𝑥 2 −14𝑥−5=0 for 𝑥
A) 𝑥=− 1 3 or 𝑥=−5
B) 𝑥=− 1 3 or 𝑥=5
C) 𝑥= 1 3 or 𝑥=−5
D) 𝑥= 1 3 or 𝑥=5

4. Problem 3 – Multiple Choice
An equation in the form 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 is solved by the quadratic formula. The solution to the equation is shown below. What are the values of a, b, and c in the quadratic equation?
𝑥= −5±

5. Problem 4 – Multiple Choice
Which quadratic equation has −7± as its roots?
A) 𝑥 2 +7𝑥+3=0
B) 𝑥 2 −7𝑥−3=0
𝑥 2 +7𝑥−3=0
D) 𝑥 2 −7𝑥+3=0

6. Problem 5 – Multiple Choice
What are the solutions to the quadratic equation 𝑥 2 −6𝑥+4=0? Please fully simplify your answer.

7. Problem 6 – Multiple Choice
What are the roots of the equation 2 𝑥 2 −5𝑥+1=0?

8. Problem 7 – Multiple Choice
In solving the quadratic equation 𝑥 2 +4𝑥−6=0 by completing the square, the following steps are given. To continue solving by completing the square, what should be Step 3?
Step 1: 𝑥 2 +4𝑥=6
Step 2: 𝑥 2 +4𝑥+4=6+4
Step 3: ?
A) 𝑥+2=10 B) 𝑥−2 2 =10
C) 𝑥+2 2 =10 D) (𝑥+2)(𝑥−2)=10

9. Problem 8 – Multiple Choice
Curtis solves the quadratic equation 𝑥 2 +12𝑥+32=0 by completing the square. His work is shown below.
Step 1: 𝑥 2 +12𝑥=−32
Step 2: 𝑥 2 +12𝑥+36=−32+36
Step 3: 𝑥+6 2 =4
Step 4: ?
What should step 4 be?

10. Problem 9 – Multiple Choice
A ball is thrown from the top of a building 240 feet tall. The height, ℎ, of the ball 𝑡 seconds after being thrown is given by the equation ℎ(𝑡) =−16 𝑡 2 +32𝑡 After how many seconds will the ball hit the ground?

11. Problem 10 – Multiple Choice
What is the solution set to the equation 𝑥−3 2 =49 ?

12. Problem 11 – Multiple Choice
Which equation represents the vertex form of = 𝑥 2 −8𝑥+23 ?
A) 𝑦= 𝑥−4 2 −7
B) 𝑦= 𝑥
C) 𝑦= 𝑥−
D) 𝑦= 𝑥−

13. Problem 12 – Multiple Choice
Which statement is true about the tables of data shown?
A) Table 1 shows quadratic behavior while Table 2 shows linear behavior.
B) Both Table 1 and Table 2 show quadratic behavior.
C) Table 1 shows exponential behavior while Table 2 shows quadratic behavior.
D) Table 1 shows linear behavior while Table 2 shows quadratic behavior.
Table 1 𝑥 −3 −2 −1 1 𝑦
1.5 2
2.5 3
Table 2 𝑥 −2 −1 1 2 𝑦 4 6

14. Problem 13 – Multiple Choice
Which answer choice demonstrates a correct method for simplifying ?
A) =4+ 10
B) ∙ 16 =5 16
C) ∙ 10 =4 10
D) ∙ 10 =16 10

15. Problem 14 – Multiple Choice
State the value of the discriminant of −5 𝑥 2 +3𝑥=−4. Then, determine the number of solutions to the quadratic equation:
Discriminant:
Number of Real Solutions:

16. Problem 15 – Multiple Choice
Determine the number of real solutions to the following quadratic equations. Please answer this for both (A) and (B)
A) 2 𝑥 2 −7𝑥+6=0 B) 9 𝑥 2 −6𝑥+1=0

17. Problem 16 - Multiple Choice
What is the square root of 45? Please simplify completely.

18. Problem 17 – Multiple Choice
What is the solution set of the equation 𝑥 2 −75=0? Please simplify completely.

19. Problem 1a – Free Response
𝑓 𝑥 = 2 𝑥
𝑔 𝑥 = 𝑥−2 2
ℎ 𝑥 =2𝑥+2
Which function has the greatest output value when 𝑥=0 ? Circle your answer choice below:
A) Linear
B) Quadratic
C) Exponential

20. Problem 1b – Free Response
𝑓 𝑥 = 2 𝑥
𝑔 𝑥 = 𝑥−2 2
ℎ 𝑥 =2𝑥+2
Which function has the greatest output value when 𝑥=2 ?
A) Linear
B) Quadratic
C) Exponential

21. Problem 1c – Free Response
𝑓 𝑥 = 2 𝑥
𝑔 𝑥 = 𝑥−2 2
ℎ 𝑥 =2𝑥+2
Predict which function will have the greatest output value when 𝑥 =50 and explain why.
A) Linear
B) Quadratic
C) Exponential

22. Problem 3 – Free Response
Directions: A vertical motion model is given by the equation ℎ 𝑡 =−16 𝑡 2 +𝑣𝑡+𝑠 where ℎ is the height of an object at any time 𝑡.
At what time(s) will the ball be 55 feet above the ground?