Quadratic Equations

2013 December(71E) Math Question 2

2. For what value(s) of x is (x + 3)(x — 4) = 0 true?

2014 December(72G) Math Question 2

2015 June(73C) Math Question 3

2010 June(68C) Math Question 3

2012 April(70G) Math Question 5

5. The expression (4c − 3d)(3c + d) is equivalent to:

Equivalent expressions

FOIL method

2021 April(Z04) Math Question 5

2013 December(71E) Math Question 7

Which of the following expressions is equivalent to (3x − 9)²?

2025 October(J08) Math Question 7

2019 June(72F) Math Question 8

2020 July(C01) Math Question 9

2009 June(67C) Math Question 9

2011 June(69F) Math Question 10

11. Which of the following expressions is equivalent to (3x + 6)(2x — 1) ?

2015 June(73C) Math Question 11

If x > 0 and 2x² + 5x = 3, what is the value of x?

35 February(Z14) Math Question 12

2023 September(G01) Math Question 12

Mary throws a stone from the edge of a cliff. While the stone is in flight, the equation h = 300 − 30t − 16t² gives the height above the ground, h feet, of the stone at any given time t seconds after being thrown. What is the height, in feet, of the stone exactly 3 seconds after Mary throws the stone?

2024 June(G20) Math Question 12

13. What is the sum of the 2 solutions of the equation X2+ x — 30 = 0 ?

2018 June(A11) Math Question 13

13. The polynomial 45x2 + 26x — 8 is equivalent to the product of (5x + 4) and which of the following binomials?

2016 December(74H) Math Question 13

2010 April(68G) Math Question 14

2021 June(D06) Math Question 14

14. What is the sum of the 2 solutions of the equation x2 − 4x − 45 = 0 ?

Quadratic equations

Roots of Quadratic Equation

2021 December(E23) Math Question 14

If (x + k)² = x² + 88x + k², then k = ?

2023 April(F11) Math Question 14

2012 December(71A) Math Question 15

2019 April(B04) Math Question 16

16. A high school ice hockey conference that consists of 10 teams requires that every conference team must play each of the other conference teams at least once in a season. For n teams in the conference, the number of conference games played in a season must then be at least n 2— n . What is the minimum number of conference games that must be played in a season for this conference?

2014 December(72G) Math Question 16

An object is launched vertically at 49 meters per second from a 980-meter high platform. The equation for the object's height, h, at time t seconds after launch is h(t) = −4.9t² + 49t + 980, where h is in meters. What will be the height, in meters, of the object 6 seconds after launch?

2024 September(H11) Math Question 16

Which of the following expressions is equivalent to x² − 13x + 30?

2024 December(H31) Math Question 16

2011 April(67F) Math Question 17

2010 December(69A) Math Question 17

17. What is the solution set to the equation x2 − x = 12 ?

Sets

2021 April(D05) Math Question 17

2019 April(Z15) Math Question 18

2019 December(C03) Math Question 18

Which of the following binomials is a factor of x² − x − 156?

2024 September(H11) Math Question 18

Let (3x − 1)(2x − 5) = ax² + bx + c. What is the value of a + b + c?

35 February(Z14) Math Question 20

2010 December(69A) Math Question 21

23. For what 2 values of x is the equation x2 — 5x + 6 = 0 true?

2015 April(73G) Math Question 23

2009 April(66F) Math Question 23

23. 'Which of the following expressions is a factored form ofx2-5x+6?

2013 June(71C) Math Question 23

If x² − 5x − 6 = 0, what is the sum of the 2 possible values of x?

2024 June(G20) Math Question 23

2011 April(67F) Math Question 24

26. An artist makes a profit of (500p — p^2) dollars from selling p paintings. What is the fewest number of paintings the artist can sell to make a profit of at least $60,000 ?

2014 June(72C) Math Question 26

2013 December(71E) Math Question 26

The graph of the function f(x) = −9(x + 1)² + 81 has its vertex at point (−1,81) and intersects the x-axis at points (−4,0) and (a,0). What is the value of a?

2024 June(G20) Math Question 26

27. Which of the following expressions is a factor of x3 - 64 ?

2017 April(74F) Math Question 27

2009 April(66F) Math Question 27

27. When (3x − 2)4 is expanded and the like terms are combined, what is the coefficient of the x4 term?

Expand a binomial to the fourth degree

2021 April(D05) Math Question 27

For real constants a, b, and c, the graph in the standard (x,y) coordinate plane below is represented by an equation in one of the following forms. Which one?

2024 September(H11) Math Question 27

28. Elmhurst Street is a two-way street. In each direction, it has one 12-foot-wide lane for car traffic, one 6-foot-wide bike lane, and one 8-foot-wide parking lane. How many feet wide is Elmhurst Street?

2017 December(A10) Math Question 28

2019 June(72F) Math Question 28

28. Which of the following most precisely describes the roots of the equation 5×2 + 7x + 2 = 0 ?

2018 April(A09) Math Question 28

The expression (x + by)⁵ will be expanded and like terms will be combined. The resulting terms will be arranged in descending powers of x. After these steps are done, the 2nd term will be 8x⁴y. What will be the total number of terms?

2025 October(J08) Math Question 28

29. Which of the following expressions is a factor of the polynomial x^2 — x — 72 ?

2015 December(72E) Math Question 29

30. Which of the following expressions is equivalent to (2x -3)(—x — 7) ?

2014 April(71H) Math Question 30

2009 April(66F) Math Question 30

31. The equation y = ax^2 + bx + c is graphed in the standard (x,y) coordinate plane below for real values of a, b, and c. When y = 0, which of the following best describes the solutions for x ?

2014 June(72C) Math Question 31

2010 June(68C) Math Question 33

33. The function P(x) = x3 − 10x2 + 9x − 90, where x is the number of items sold, models the profit  P(x), in dollars, for Company A. The company breaks even when the profit is $0. How many items must Company A sell to break even?

Factoring cubic polynomials

2021 April(D05) Math Question 33

33. Which of the following values is a zero of f(x) = 2x 5x2 — 12x ?

2013 June(71C) Math Question 33

34. The quadratic formula gives the 2 roots for the equation axe + bx + c = O. What are the 2 roots of the equation 3×2 — x = 10 ?

2014 April(71H) Math Question 34

Which of the following expressions is equivalent to (y + 8)³?

2024 April(Z13) Math Question 34

2019 April(B04) Math Question 35

2009 April(66F) Math Question 36

2019 December(C03) Math Question 37

A factor of 2.5x² − 30x + c is x + 4. What is the value of c?

2025 October(J08) Math Question 37

2012 June(70C) Math Question 38

2020 July(C01) Math Question 39

40. What is the set of real solutions for |x|^2— |x| — 2 = 0 ?

2015 December(72E) Math Question 40

2009 December(68A) Math Question 41

41. The equation 24x2 + 2x = 15 has 2 solutions. What is the greater of the 2 solutions?

2021 April(Z04) Math Question 41

2010 April(68G) Math Question 43

2013 December(71E) Math Question 44

47. Which of the following binomials is a factor of 3x^2 + 11x — 4 ?

2014 December(72G) Math Question 47

2018 December(B05) Math Question 47

2020 June(C02) Math Question 48

49. What is the solution set of the equation
x4 +21x 2 -100=0?

2019 June(B02) Math Question 49

2013 December(71E) Math Question 49

50. One of the following values is equal to f (5a). Which one?

2021 April(Z04) Math Question 50

2012 April(70G) Math Question 52

2010 December(69A) Math Question 52

52. Given that (x + 2) and (x — 1) are factors of the quadratic expression below, what are the values of a and b ?

2015 June(73C) Math Question 52

53. The height above the ground, h units, of an object seconds after being thrown from the top of a building is given by the equation h = —2t2 + 10: + 48. An equivalent factored form of this equation shows that the object:

2015 June(73C) Math Question 53

53. Which of the following is a quadratic equation that has

2014 June(72C) Math Question 53

2010 June(68C) Math Question 53

54. A polynomial in x has m nonzero terms. Another polynomial in x has n nonzero terms, where m < n. These polynomials are multiplied and all like terms are combined. The resulting polynomial in x has a maximum of how many nonzero terms?

2013 June(71C) Math Question 54

2013 April(71G) Math Question 55

2009 December(68A) Math Question 55

56. One of the following equations is that of a parabola
with x-intercepts −5 and _3_ in the standard (x,y) 4
coordinate plane. Which equation?

2021 June(D06) Math Question 56

For what positive value of k will the expression 9x² + kx + 25 factor into the form (ax + b)² for some real number a and some real number b?

2023 September(G01) Math Question 58

A parabola that contains the points (0,−3), (−2,0), and (3,0) is shown in the standard (x,y) coordinate plane below. The function f has the graph of this parabola translated 3 coordinate units right. Which of the following is the output of f(x)?

2024 December(H31) Math Question 58

58. For what values of b does the equation x2 + bx + 1 = 0 have no real solutions?

2020 December(D03) Math Question 58

2019 April(Z15) Math Question 59

2009 June(67C) Math Question 59

59. When (x+1)4 is expanded and the like terms are combined, what is the coefficient of the x2term?

2020 July(C01) Math Question 59

59. The graph in the standard (x,y) coordinate plane below is the graph of one of the following functions. Which one?

2017 June(74C) Math Question 59

2012 December(71A) Math Question 59

2011 April(67F) Math Question 60

Complex Number

2010 June(68C) Math Question 60

60. Which of the following quadratic equations has the complex number (1 + V-1) as a solution?

2018 April(A09) Math Question 60

60. One solution of the equation 4×3 — 212 + x + 7 = 0 is x = —1. Which of the following describes the other 2 solutions?

2017 December(A10) Math Question 60

60. What is the minimum degree possible for the polynomial function whose graph is shown in the standard (x,y) coordinate plane below?

Quadratic EquationsThere are 102 ACT math questions under Quadratic Equations

Sub-topics

2013 December(71E) Math Question 2

2014 December(72G) Math Question 2