A. B. C. D. Quadratics Practice Test. Question 1. Select the graph of the quadratic function. g (x ) = 1 3 x 2. 3/8/2018 Print Assignment

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1 Question 1. Select the graph of the quadratic function. g (x ) = 1 3 x 2 C. D. 1/24

2 Question 2. Describe the transformations necessary to get from the graph of the parent function f (x ) = x 2 to the graph of the given function. g (x ) = 3(x 9) (select) the graph vertically by a factor of, then translate the graph units to the (select) and units (select). 2/24

3 Question 3. Rewrite the function in standard form. f (x ) = 3(x 4) The standard form of f (x ) = 3(x 4) is 3/24

4 Question 4. If the only information you have about a parabola is the location of its vertex, what other characteristics of the graph do you know? You know the axis of symmetry, which goes through the (select) of the vertex. You also know that the y -coordinate of the vertex is (select) of the parabola. 4/24

5 Question 5. Consider the graph of f (x ) = 2 3 (x 3)2. Choose True or False for each statement about the graph. The vertex is (3, 0). True False The minimum value is 0. True False The axis of symmetry is x = 2 3. True False 5/24

6 Question 6. Enter f (x ) = 2(x 5) in standard form. In which form is it easier to determine the maximum value of the graph? Complete the explanation. f (x ) = ; It is easier to find the maximum value when the equation is in (select). The vertex is (, ), so the maximum value is. 6/24

7 Question 7. Find the zeros of the function. f (x ) = x (x 66) The zeros of the function are. 7/24

8 Question 8. Find the zeros of the function. f (x ) = 2x (x + 9) + 10x + 90 The zeros of the function are. 8/24

9 Question 9. Solve the equation. x 2 9x 22 = 0 The solutions are. 9/24

10 Question 10. Solve the equation. 49x = 0 The solutions are. 10/24

11 Question 11. A golfer hits a ball from a starting elevation of 2 feet with a velocity of 70 feet per second down to a green with an elevation of 7 feet. The number of seconds t it takes the ball to hit the green can be represented by the equation 16t t + 2 = 7. How long does it take the ball to land on the green? It takes the ball seconds to land on the green. 11/24

12 Question 12. Consider the equation 5x (2x + 1) 3(2x + 1) = 0. Choose True or False for each statement about the equation. It is equivalent to (5x 3)(2x + 1) = 0. True False A solution of the equation is x = 1 2. True False A zero of the equation is 3 5. True False 12/24

13 Question 13. Part 1 Marcello is replacing a rectangular sliding glass door with dimensions of (x + 7) and (x + 3) feet. The area of the glass door is 45 square feet. What are the length and width of the door? Complete the explanation of how you got your answer. I found the area of the glass door by multiplying the length by the width, which is. I set this product, which represents the area in terms of x, equal to side was 0 and solved for x and got. Then, I rewrote the equation so one. A dimension of the door (select) be negative so x =. Part 2 The length of the door is 2 + 7, or feet, and the width is 2 + 3, or feet. 13/24

14 Question 14. Find the discriminant of the quadratic equation, and determine the number of real solutions of the equation. 2x 2 + 8x = 9 The discriminant is. The number of real solutions of the equation is. 14/24

15 Question 15. Solve the equation using the given method. 7x 2 28 = 0; square root The solutions are. 15/24

16 Question 16. A quadratic equation has the zeros 3 and 6. Can the quadratic equation be the given equation? A. (2x + 6)(x 6) = 0 Yes No B. (6x 1) (x + 3) = 0 Yes No C. 3x (x 6) = 0 Yes No 16/24

17 Question 17. Factor and solve each equation. Does the equation have a solution of x = 5? A. 3x x 5 = 0 Yes No B. x 2 + 3x 40 = 0 Yes No C. x 2 3x 40 = 0 Yes No 17/24

18 Question 18. The area of a square table top can be represented by (9x 2 30x + 25) ft 2. The perimeter of the table top is 34 feet. What is the value of x? Complete the explanation of how you solved this problem. Each side of the table is ft long. I factored (9x 2 30x + 25) which is a perfect square trinomial. Each side of the table is also ( x ) ft long. I set the two expressions for side length equal to each other and solved to find that x =. 18/24

19 Question 19. Consider the graph of f (x ) = 2x 2 1. Determine if each statement is True or False. 2 A. The vertex is ( 2, 1 2). True False B. The maximum value is 1 2. True False C. The axis of symmetry is x = 2. True False 19/24

20 Question 20. Does the given statement describe a step in the transformation of the graph of f (x ) = x 2 that would result in the graph of g (x ) = 5(x + 2) 2? A. The parent function is reflected across the x -axis. Yes No B. The parent function is stretched by a factor of 5. Yes No C. The parent function is translated 2 units up. Yes No 20/24

21 Question 21. Solve 2x x + 5 = 0. Is each of the following a solution of the equation? A. x = 1 3 Yes No B. x = 5. Yes No C. x = 2 3 Yes No 21/24

22 Question 22. Select the graph that shows y = 2x x 31. What is the axis of symmetry of the graph? What is its vertex? C. D. The axis of symmetry is x =. The vertex is 22/24

23 Question 23. Select the graph that shows t (x ) = 1 (x + 2)(x 4), and enter the function in standard form. 2 C. D. The function in standard form is t (x ) = 23/24

24 Question 24. Solve 4x 2 + 8x = 3. Use completing the square and complete the explanation for why you would use completing the square to solve the given equation. Complete the work. Part 1 I would complete the square because is a perfect square. Part 2 4x 2 + 8x = 3 4x 2 + 8x + = 3 + Part 3 (2x + ) 2 = 1 Part 4 2x + 2 = 1 or 2x + 2 = Part 5 x = or x = 24/24