Unit 6 Part 2 Test Review Algebra 1

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

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

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± 17 4

Problem 4 – Multiple Choice Which quadratic equation has −7± 61 2 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

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

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

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

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?

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+240. After how many seconds will the ball hit the ground?

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

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

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

Problem 13 – Multiple Choice Which answer choice demonstrates a correct method for simplifying 160 ? A) 16 + 10 =4+ 10 B) 10 ∙ 16 =5 16 C) 16 ∙ 10 =4 10 D) 16 ∙ 10 =16 10

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:

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

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

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

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

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

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

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?