CC Algebra Quadratic Functions Test Review. 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1?

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1 Name: CC Algebra Quadratic Functions Test Review Date: 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1? a. c. c. b. d. Which statement best describes the change in this graph when the coefficient of x 2 is multiplied by 4? a. The parabola becomes wider. b. The parabola will shift up 4 units. c. The parabola becomes narrower. d. The parabola will shift right 4 units. 2. Which point is not on the graph represented by y = x 2 + 3x 6? 5. The equation y = ax 2 + bx + c is graphed on the set of axes below. a. (-6, 12) c. (2, 4) b. (-4,-2) d. (3,-6) 3. The graph below represents the parabolic path of a ball kicked by a young child. What are the vertex and the axis of symmetry for the parabola? Based on the graph, what are the roots of the equation ax 2 + bx + c? a. 0 and 5 c. 1 and 5 b. 1 and 0 d. 3 and -4 a. Vertex: (3, 8), axis of symmetry: x = 3 b. Vertex: (8, 3), axis of symmetry: x= 3 c. Vertex: (3, 8), axis of symmetry: y = 3 d. Vertex: (8, 3), axis of symmetry: y= 3

2 6. The roots of the equation 2x = 9x are a. Real, rational, and equal b. Real, irrational, and unequal c. Real, rational, and unequal d. Imaginary 7. What is the vertex of the graph of the equation y = 3x 2 + 6x + 1? a. (-1,-2) c. (1,-2) b. (-1, 10) d. (1, 10) 8. What is the solution of the system of equations y x = 5 and y = x 2 + 5? 9. The discriminant of a quadratic equation is 24. The roots are a. Imaginary b. Real, rational, and unequal c. Real, rational, and equal d. Real, irrational, and unequal 10. The graph of a parabola is represented by the equation y = ax 2 where a is a positive integer. If a is multiplied by 2, the new parabola will become a. narrower and open downward b. wider and open downward c. narrower and open upward d. wider and open upward a. (0, 5) and (1, 6) c. (2, 9) and ( 1, 4) b. (0, 5) and ( 1, 6) d. ( 2, 9) and ( 1, 4) 11. A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it with a width of x meters, as shown in the diagram below. Together, the walkway and the garden have an area of 396 square meters. Write an equation that can be used to find x, the width of the walkway. Describe how your equation models the situation. State the width of the walkway, in meters.

3 12. The function f(x) is graphed on the set of axes below. On the same set of axes, graph f(x +1) Find the roots of the equation x 2 + x = 8 x graphically. 14. Alicia and Brent were comparing the vertex of two quadratic functions. Brent stated that f(x) and g(x) have different maximum values. Alicia thinks that both functions have a maximum of 6. Is either of them correct? Explain your choice. g(x) = x 2 + 3x + 4

4 15. Complete the square to find the vertex of the equation y = x 2 8x Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the parabola whose equation is y = 2x 2 8x A contractor needs 54 square feet of brick to construct a rectangular walkway. The length of the walkway is 15 feet more than the width. Write an equation that could be used to determine the dimensions of the walkway. Solve this equation to find the length and width, in feet, of the walkway. 18. Three brothers have ages that are consecutive even integers. The product of the first and third boys ages is 20 more than twice the second boy s age. Find the age of each of the three boys. 19. Given the function p(x) includes the point (0, 5). What are the coordinates of the point after the shift of p(x) 2? 20. Given the function m(x) includes the point (-3, -4). What are the coordinates of the point after the shift of m(x + 4)?

5 21. The path of a rocket fired during a fireworks display is given by the equation s(t) = 64t 16t 2, where t is the time, in seconds, and s is the height, in feet. What is the maximum height, in feet, the rocket will reach? [only an algebraic solution will be accepted] In how many seconds will the rocket hit the ground? [only an algebraic solution will be accepted] 22. Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation h = -8t t, where h is the height, in feet, and t is the time, in seconds. Fill in the table of values which could be used to graph the path of the ball: t h What is the value of t at which h has its greatest value? What is the maximum height that the ball reaches? 23. Solve the following system of equations algebraically: y = x 2 6x + 9 y = 9x + 19

6 24. Let f(x) = x 2 + 4x 5 and g(x) = 2x +3. On the set of axes below, draw the graphs of y = f(x) and y = g(x). Using this graph, determine and state all values of x for which f(x) = g(x). 25. On the set of axes below, solve the system of equations graphically and state the coordinates of all points in the solution. y = (x 2) 2 3 2y + 16 = 4x