Quadratic Equations Practice Test Questions And Answers - Quiz
Think you can conquer those tricky quadratic equations? Ready to solve for x and master the art of factoring? Then step up to the challenge with our Quadratic Equation Quiz! This quiz is designed to test your understanding of quadratic equations and their solutions. We'll cover a range of topics, including factoring quadratic expressions, using the quadratic formula, solving word problems, and graphing parabolas.
If you want to learn about Quadratic Equations this practice test helps you practice without the pressure of an exam! You'll get instant feedback on your answers and helpful explanations to reinforce your understanding. If you're Read morea student preparing for a test, an adult brushing up on your math skills, or just a math enthusiast looking for a challenge, this quiz is perfect for you.
Quadratic Equations Test Questions and Answers
- 1.
-1x2 + 0x + 49 = 0
- A.
X = -9 and -6
- B.
X = 7 and -7
- C.
X = 8 and 3
- D.
X = 7 and -3
- E.
X = 9 and -9
Correct Answer
B. X = 7 and -7Explanation
The given equation is a quadratic equation of the form ax^2 + bx + c = 0. By factoring or using the quadratic formula, we can find the values of x that satisfy the equation. In this case, the equation can be factored as (x - 7)(x + 7) = 0, which means that x = 7 and x = -7 are the solutions to the equation.Rate this question:
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- 2.
-1x2 + 2x + 48 = 0
- A.
X = -2 and 1
- B.
X = -1 and -7
- C.
X = 9 and -9
- D.
X = 8 and -8
- E.
X = 8 and -6
Correct Answer
E. X = 8 and -6Explanation
Standard Form: The equation is already in standard quadratic form: ax² + bx + c = 0, where a = -1, b = 2, and c = 48.
Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
Substitute Values: x = (-2 ± √(2² - 4 * -1 * 48)) / 2 * -1 x = (-2 ± √(4 + 192)) / -2 x = (-2 ± √196) / -2 x = (-2 ± 14) / -2
Solve for the two possible values of x: x₁ = (-2 + 14) / -2 = 12 / -2 = -6 x₂ = (-2 - 14) / -2 = -16 / -2 = 8
Therefore, the solutions to the quadratic equation are x = 8 and x = -6.Rate this question:
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- 3.
1x2 + 5x - 14 = 0
- A.
X = -1 and 2
- B.
X = -1 and 2
- C.
X = -7 and 2
- D.
X = 9 and -9
- E.
X = 9 and -9
Correct Answer
C. X = -7 and 2 -
- 4.
1x2 + 10x + 21 = 0
- A.
X = -7 and -3
- B.
X = -7 and 3
- C.
X = 8 and -6
- D.
X = 8 and 6
- E.
X = 10 and 11
Correct Answer
A. X = -7 and -3 -
- 5.
-1x2 + 3x + 28 = 0
- A.
X = -6 and -8
- B.
X = 9 and 4
- C.
X = 6 and -5
- D.
X = -7 and -4
- E.
X = 7 and -4
Correct Answer
E. X = 7 and -4 -
- 6.
What is the vertex of the following equation: x2 - 8x + 15 = 0?
- A.
(4,1)
- B.
(4,-1)
- C.
(-4,-1)
- D.
(-4,1)
Correct Answer
B. (4,-1)Explanation
The vertex of a quadratic equation in the form of y = ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)). In this equation, a = 1, b = -8, and c = 15. Plugging these values into the formula, we get (-(-8)/2(1), f(-(-8)/2(1))). Simplifying further, we get (4, f(4)). To find the y-coordinate, we substitute x = 4 into the equation: 4^2 - 8(4) + 15 = 1. Therefore, the vertex is (4, -1).Rate this question:
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- 7.
What is the axis of symmetry and range of the following function: x2 - 8x + 15 = 0?
- A.
Axis: x=4 ; Range: (-1,infinity)
- B.
Axis: x=-4 ; Range: (-1, infinity)
- C.
Axis: x=-1 ; Range: (4, infinity)
- D.
Axis: x=-1 ; Range: (-4, infinity)
Correct Answer
A. Axis: x=4 ; Range: (-1,infinity)Explanation
The given quadratic function is in the form of f(x) = x^2 - 8x + 15. To find the axis of symmetry, we can use the formula x = -b/2a, where a, b, and c are coefficients of the quadratic equation. In this case, a = 1 and b = -8. Substituting these values into the formula, we get x = -(-8)/2(1), which simplifies to x = 4. Therefore, the correct answer is "Axis: x=4".
To find the range of the function, we need to determine the set of all possible y-values that the function can produce. Since the coefficient of x^2 is positive, the parabola opens upward and the minimum value occurs at the vertex. The y-coordinate of the vertex can be found by substituting the x-coordinate of the axis of symmetry (4) into the function. f(4) = (4)^2 - 8(4) + 15 = 16 - 32 + 15 = -1. Hence, the range of the function is (-1, infinity). Therefore, the correct answer is "Range: (-1, infinity)".Rate this question:
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- 8.
What is the vertex of the following equation: -x2 - 9x - 8 = 0?
- A.
(-4.5, 12.25)
- B.
(-1,-4.5)
- C.
(-1,9)
- D.
(1,9)
Correct Answer
A. (-4.5, 12.25)Explanation
The vertex of a quadratic equation in the form of y = ax^2 + bx + c can be found using the formula x = -b/2a. In this equation, a = -1 and b = -9. Plugging these values into the formula, we get x = -(-9)/2(-1) = 9/-2 = -4.5. To find the y-coordinate of the vertex, we substitute this value of x back into the equation: y = -(-4.5)^2 - 9(-4.5) - 8 = -20.25 + 40.5 - 8 = 12.25. Therefore, the vertex is (-4.5, 12.25).Rate this question:
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- 9.
What is the range of the following function: -x2 + 2x + 8 = 0?
- A.
(infinity, 9)
- B.
(-infinity, infinity)
- C.
(9, infinity)
- D.
(-9, infinity)
- E.
(-infinity, 9)
Correct Answer
E. (-infinity, 9)Explanation
For the given quadratic function -x2 + 2x + 8 = 0, it forms a downward-opening parabola. This means that the highest point of the parabola, known as the vertex, represents the maximum value of the function.
By calculating the vertex of the parabola, we find that it occurs at the point (1, 9), where the x-coordinate is 1 and the y-coordinate (or function value) is 9.
Since the parabola opens downwards, the maximum value of the function is 9. Therefore, the range of the function consists of all real numbers less than or equal to 9. In simpler terms, the function's range includes all values from negative infinity up to and including 9.Rate this question:
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- 10.
What is the domain of the following function: -x2 + 2x + 8 = 0?
- A.
(1,9)
- B.
(-infinity,infinity)
- C.
(infinity,9)
- D.
(1, infinity)
- E.
(9,infinity)
Correct Answer
B. (-infinity,infinity)Explanation
The function -x^2 + 2x + 8 = 0 is a quadratic equation. The domain of a quadratic equation is always the set of all real numbers, which means that the function is defined for any value of x. Therefore, the correct answer is (-infinity, infinity).Rate this question:
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Nov 18, 2024Quiz Edited by
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Expert Reviewed by
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Apr 20, 2010Quiz Created by
Mmmaxwell
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