1. (7A) Points (3, 2) and (7, 2) are on the graphs of both quadratic functions f and g. The graph of f opens downward, and the graph of g opens upward. Which of these statements are true? I. The graphs of f and g have the same axis of symmetry. II. The graphs of f and g have the same x-intercepts. III. The graph of f has a maximum point, and the graph of g has a minimum point. IV. The graph of f is the result of a reflection of the graph of g over the x-axis. A I only B II only C II and IV D I and III 2. (6B) A quadratic function is graphed on the grid. If this function is written in the form y = a (x - h) 2 + k, what is the value of a? A. 2 B. 5 C. -8 D. -3 3. (6C) When a contractor paints a square surface that has a side length of x feet, he needs to know the area of the surface in order to buy the correct amount of paint. Since the contractor always adds 25 square feet to the area, he buys extra paint. Which function can be used to find the total area in square feet, A(x), that the contractor will use to determine how much paint he needs to buy? A A(x) = 25x 2 B A(x) = (25 + x) 2 C A(x) = (25x) 2 D A(x) = x 2 + 25 4. (6C) The graph models A, the area in square feet of a rectangular porch with a length that is 0.56w less than 28 ft given a width of w feet. Based on the graph, what is the width in feet of the porch with the greatest area? F. 175 ft G. 50 ft H. 25 ft J. 350 ft
5. (6C) A function is graphed below. Which function is best represented by this graph? A. f(x) = (x 1) 2 + 4 B. f(x) = x 2 + 4x + 3 C. f(x) = (x + 1) 2 + 4 D. f(x) = (x 4) 2 3 6. (6B) Which function s graph has a vertex of (-3, -5) and contains the point (7, 5)? A. y = 1 10 (x + 3)2 5 B. y = 1 10 (x 3)2 5 C. y = 2(x + 3) 2 + 5 D. y = 2(x 3) 2 + 5 7. (6A) A baseball is tossed upward from the ground. The height of the ball in feet can be modeled by the function y = -3x(x-6) where x is the time in seconds after the ball is released. A. What is the maximum height of the ball? B. Approximately how long it takes the ball to hit the ground? 8. (7A) A table of values for the quadratic function g(x) is shown below. Which of the statements below about the graph of g are true? (use the grid to help you solve it) I. The graph has a line of symmetry at x = 2 II. The graph contains the point (3, -15) III. The graph has an x-intercept at (6, 0) IV. The graph has a vertex at (1, -15) A. I and II only B. III and IV only C. I, II, and III only D. all are true
9. (7C) Which statement about the quadratic parent function is true? F. Its graph is symmetrical about the x-axis. G. Its graph is symmetrical about the y-axis. H. Its domain is the set of all non-negative numbers. J. Its range is the set of all real numbers 10. (6C) The population of a town is currently 9,000. The function p = 9,000 + 8t 2 can be used to estimate p, the population of the town t years from now. Based on this function, which statement is true? F. The population of the town is increasing at a constant rate. G. The population of the town will reach 10,000 between 11 and 12 years from now. H. The population of the town will increase by 256 people two years from now. J. The population of the town will increase and then decrease. 11. (7C) Which statements about the quadratic functions below is true? f(x) = x 2 + 64 g(x) = 2x 2 51 h(x) = x 2 + 14 A. The graphs of all three of these functions have a minimum point. B. The graphs of all these functions have the same axis of symmetry. C. The graph of all three functions do not cross the x-axis. D. The graphs of all these functions have the same y-intercepts. 12. (6C) Two points on the graph of a quadratic function are shown on the grid below. What is the equation for the axis of symmetry of the graph of this function? A. x = 3 B. y = 3 C. x = 5 D. y = 5
13. (7B) What are the solutions to: 8x(7 x) + 1 (7 x) = 0? 5 14. How do you write the function f(x) = 4(x 2) 2 + 8 in standard form? A. f(x) = 4x 2 16x 8 B. f(x) = 4x 2 + 16x + 24 C. f(x) = 4x 2 16x + 24 D. f(x) = 4x 2 + 16x 8 15. What is the maximum value of: f(x) = 3(x + 3) 2 + 4? 16.
17. 18 19. 20.
21. 22. 23. (A.6A) What is the range of f(x) = x 2 + 1? A. All real numbers B. All real number greater than or equal to 0 C. All real numbers greater than or equal to 1 D. All real numbers less than or equal to 1 24. (A.7A) The graph models A, the area in square feet of a rectangular porch with a length that is 0.56w less than 28 ft given a width of w feet. Based on the graph, what is the width in feet of the porch with the greatest area? A. 175 ft B. 50 ft C. 25 ft D. 350 ft
Day 9 Cat 4 1. D 2. A 3. D 4. H 5. C 6. A 7. A.)27 FT; B.) 6 SEC 8. D 9. G 10. G 11. B 12. A 13. C 14. C 15. 4 16. B 17. B 18. B 19. A 20. B 21. C 22. C 23. C 24. C