University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2020
Views:

254

Pages:

2
Author:

omiliar74be

**Module 4.3: Quiz Review** **Name** **KEY** Match the equations with their solutions. SHOW YOUR WORK!!!!! 1. a. (4, 3) (-4, -3) b. (0, -4) (-3, -7) c. (4, 0) d. no solution 2. a. (4, 3) (-4, -3) b. (0, -4) (-3, -7) c. (4, 0) d. no solution Solve each system represented by the functions graphically. 5. y = -(x + 2)² + 4 y = x - 5 [Image of a graph with solutions (-1, -6) and (5, 0)] 6. y = x² + 2x + 6 y = -x + 6 [Image of a graph with solution (0, 6)] Solve each system algebraically. 7. y = x² + 4 y = x - 5 x² + 4 = x - 5 x² - x + 9 = 0 (0, 4) (-5, 0) 8. y = x² + 6 y = -x + 6 x² + 6 = -x + 6 x² + x = 0 x(x + 1) = 0 x = 0 or x = -1 (0, 6) (-1, 7) 9. Jason is driving his car on a highway at a constant rate of 60 miles per hour when he passes his friend Alan whose car is parked on the side of the road. To catch up to Jason's passing car, Alan accelerates at a constant rate. The distance d, in miles, that Alan's car travels as a function of time t, in hours, since Jason's car has passed is given by d = 720t². How long does it take Alan's car to catch up with Jason's car? Jason: d = 60t Alan: d = 720t² Need to find when their distance is the same 720t² = 60t 720t² - 60t = 0 60t(12t - 1) = 0 t = 0 or t = 1/12 hour 10. The flight of a cannonball toward a hill is described by the parabola y = 3 + 0.14x - 0.006x². The hill slopes upward along a path given by y = 0.15x. Where on the hill does the cannonball land? Set the equations equal to each other 0.15x = 3 + 0.14x - 0.006x² -0.15x -0.15x 0 = 3 - 0.01x - 0.006x² Rewrite: -0.006x² - 0.01x + 3 = 0 Negative time doesn't make sense. x = (-(-0.01) ± √((-0.01)² + 4(-0.006)(3))) / 2(-0.006) x ≈ 0.18 or x ≈ -27 x ≈ 0.18 11. Amy throws a quarter from the top of a building at the same time that a balloon is released from the ground. The equation describing the height y above ground of the quarter in feet is y = 54 - 2x², where x is the time in seconds. The equation describing the elevation of the balloon in feet is y = 10x + 6, where x is the time in seconds. After how many seconds will the balloon and quarter pass each other? 54 - 2x² = 10x + 6 -2x² - 10x + 48 = 0 x² + 5x - 24 = 0 (x + 8)(x - 3) = 0 x = -8 or x = 3 so 3 seconds 12. Find the missing characteristics of the parabola from the given information. Focus: (6, 0) Directrix: x = -6 Opens: Right Axis of Symmetry: y = 0 (cuts parabola in half) p: 6 (distance between vertex and focus) Vertex: (0, 0) Equation: (y - k)² = 4p(x - h) (y - 0)² = 4(6)(x - 0) y² = 24x