Unit 6 Review Day 1 – Day 2 Class Quiz Algebra 1

Problem 1 What are the coordinates of the maximum or minimum value for the graph of the function 2 𝑥 2 −8𝑥+1=𝑦? Answer: (2, −7)

Problem 2 Let 𝑓 𝑥 = 𝑥 2 +5𝑥+7. What would change if the function was changed to 𝑓 𝑥 = 𝑥 2 +5𝑥+10? A) Axis of Symmetry B) Vertex C) Direction that the parabola opens D) Domain

Problem 3 Identify the following from the graph Approximate if it’s not clear A) 𝑥-intercept(s) B) 𝑦-intercept A) −1, 0 & (4, 0) B) (0,−4)

Problem 4 A ball is thrown into the air. The graph shows the height of the ball, in feet, with respect to time, in seconds. Which of the following statements is NOT true? A) The ball is in the air for 10 seconds. B) The ball is at the same height at 2 seconds and 8 seconds. C) The ball reaches a maximum height of 20 feet. D) The ball takes the same amount of time to go up as it takes to come down.

Problem 5 Which quadratic function opens downward and has a vertex of (1, −2)? A) 𝑦= 𝑥 2 −2𝑥+3 B) 𝑦=− 𝑥 2 +2𝑥−3 C) 𝑦= 𝑥 2 +4𝑥−10 D) 𝑦=−2 𝑥 2 −𝑥+8

Problem 6 Which quadratic function opens upward and has its vertex at 𝑥=−3. A) 𝑦= 𝑥 2 +6𝑥−2 B) 𝑦=− 𝑥 2 −6𝑥+2 C) 𝑦=2 𝑥 2 −12𝑥+1 D) 𝑦=−4 𝑥 2 −9𝑥+1

Problem 7 Given the graph, identify the maximum or minimum point Answer: (−1, −2)

Problem 8 Given the equation 𝑦= 𝑥 2 +𝑏𝑥−3 and that the x-intercepts are at 1, 0 & (−3, 0), what value of 𝑏 will satisfy the equation 𝑥 2 +𝑏𝑥−3=0? Answer: 𝑏=2

Problem 9 Given the graph, identify the solutions Answer: 𝑥=−4, 𝑥=4

Problem 10 Write a function that is narrower than the graph of 𝑓 𝑥 = 𝑥 2 −5𝑥+1 Answer: Many possible solutions. The key is that there is a whole number in front of 𝑥 2 . For example, 𝑓 𝑥 =2 𝑥 2 −5𝑥+1

Problem 11 Write a function that has y-values that are 6 more than those of 𝑓 𝑥 =− 1 2 𝑥 2 +4𝑥 Answer: 𝑓 𝑥 =− 1 2 𝑥 2 +4𝑥+6

Problem 12 Write a function that has y-values that are 3 less than those of 𝑓 𝑥 =9 𝑥 2 Answer: 𝑓 𝑥 =9 𝑥 2 −3

Problem 13 Given 𝑦=𝑎 𝑥−𝑏 2 and the following graph, draw a graph that is equivalent to 𝑦=𝑎 𝑥−𝑏 2 +2 Answer: The new graph should be shifted vertically up 2 units

Problem 14 Write an equation, in Vertex form, that has the same vertex as the graph. It should not be the equation of the graph given. Answer: Many possible answers. The key is that they all have the same vertex of (−1, −3). For example 𝑦= 𝑥+1 2 −3

Problem 15 Identify the line that the given graph is symmetrical about. Answer: 𝑥=1

Problem 16 Given the graph, identify the following. A) Axis of Symmetry B) Y-Intercept C) Vertex A) 𝑥=−2 B) (0, 1) C) (−2, −3)

Problem 17 Which is the correct equation for the graph shown? A) 𝑦=3 𝑥+4 2 −1 B) 𝑦=−3 𝑥+4 2 −1 C) 𝑦=3 𝑥−4 2 +1 D) 𝑦=−3 𝑥−4 2 +1

Free Response: #1 A) Graph 𝑦=−3 𝑥 2 +6𝑥+9 B) Identify the vertex C) Identify the axis of symmetry D) Identify the domain E) Identify the range F) Identify the 𝑦-intercept Answers: 1, 12 , 𝑥=1, 𝐴𝑙𝑙 𝑟𝑒𝑎𝑙 #𝑠, 𝑦≤12, (0, 9)

Free Response: #2 Two quadratic functions are listed below. When graphed, which of the two parabolas have the greatest maximum or minimum? Support your decision mathematically. 𝑔(𝑥) 𝑓 𝑥 = 1 4 𝑥+2 2 +6 Answer: g(𝑥) has the greatest minimum. Graph both to verify 𝒙 𝒈(𝒙) 9 1 6 2 5 3 4

Free Response: #3 A) Graph 𝑦=(𝑥−2)(𝑥+4) B) Identify the vertex C) Identify the axis of symmetry D) Identify the domain E) Identify the range F) Identify the 𝑥-intercepts Answers: −1, −9 , 𝑥=−1, 𝐴𝑙𝑙 𝑟𝑒𝑎𝑙 #𝑠, 𝑦≥−9, 2, 0 & (−4, 0)

Free Response: #4 A ball is thrown with an initial velocity of 48 feet per second. Its path is modeled by the equation ℎ 𝑡 =−16 𝑡 2 +48𝑡+20 A) What is the maximum height of the ball? B) At what height was the ball released? A) Find the vertex using 𝑥=− 𝑏 2𝑎 , then plug into ℎ(𝑡). 56 feet B) Ball released at 𝑡=0. 20 feet