PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022
How much have you learned?
Quadratics
Passport to advanced math
Directions: For testlike practice, give yourself 15 minutes to complete this question set. Be sure to study the explanations, even for questions you answered correctly. They can be found at the end of this chapter.
31. A car’s fuel economy generally increases as its speed increases, but past a certain speed, it starts to drop, as depicted for a particular car in the graph above. What is the best estimate of this car’s fuel economy, in miles per gallon, at 100 miles per hour?
A. 0
B.10
C.17
D. 41
32. The x-intercepts of the equation y = x2 − 9x + 20 are m and n, where m > n. What is the value of m?
33. Shawna throws a baseball into the air. The equation h = −5(t2 − 4t + 4) + 22 represents the height of the ball in meters t seconds after it is thrown. Which of the following equations could represent the height of a second ball that was thrown by Meagan, if Meagan’s ball did not go as high as Shawna’s ball?
A. h = −10(t − 4)2 + 27
B.h = −10(t − 2)2 + 25
C.h = −8(2t − 1)2 + 23
D. h = −5(t − 2)2 + 21
34. 
Which of the following equations could represent a parabola that has a minimum value of −3 and whose axis of symmetry is the line x = 2?
A. y = (x − 3)2 + 2
B.y = (x + 3)2 + 2
C.y = (x − 2)2 − 3
D. y = (x + 2)2 − 3
35. Which of the following is a solution to the equation x2 + 24 = 14x − x2 ?
A. −3
B.
C.4
D. 7
36. Which of the following is an equivalent form of 4x2 − 8x + 64 = 0?
A. (x − 2)2 = −12
B.(x + 2)2 = 12
C.(x − 1)2 = −15
D. (x + 1)2 = 15
37. Which of the following is equivalent to 64x2 − 81y2?
A. (8x + 9y)(8x − 9y)
B.(9x + 8y)(9x − 8y)
C.(8x + 9y)2
D. (8x − 9y)2
38. Which of the following quadratics has only one real solution?
A. 4x2 = 3x − 8
B.10x = 2 − x2
C.7x2 + 2x − 5 = 0
D. 3x2 − 6x + 3 = 0
39. What is the absolute difference of the values of x for the solutions to the system of equations above?
40. Which of the following coordinates is the vertex of the parabola y = x2 − 14x + 3?
A. (7, −46)
B.(−7, −46)
C.(14, −193)
D. (−14, −193)