Q. What is the vertex of the parabola given by the equation y = 2x^2 - 4x + 1?
A.
(1, -1)
B.
(1, 0)
C.
(2, 1)
D.
(0, 1)
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Solution
To find the vertex, use the formula x = -b/(2a). Here, a = 2, b = -4, so x = 1. Substitute x = 1 into the equation to find y = -1.
Correct Answer:
A
— (1, -1)
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Q. What is the x-intercept of the line 2x + 3y = 6? (2019)
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Solution
To find the x-intercept, set y = 0. Thus, 2x = 6, giving x = 3.
Correct Answer:
A
— 2
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Q. What is the x-intercept of the line given by the equation 4x + 5y - 20 = 0?
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Solution
To find the x-intercept, set y = 0. Thus, 4x = 20, giving x = 5.
Correct Answer:
A
— 4
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Q. What is the y-intercept of the line given by the equation 2x + 5y - 10 = 0? (2019)
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Solution
Rearranging to y = (-2/5)x + 2, the y-intercept is 2.
Correct Answer:
A
— 2
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Q. What is the y-intercept of the line given by the equation 5x - 2y = 10? (2023)
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Solution
Rearranging to slope-intercept form: -2y = -5x + 10, thus y = (5/2)x - 5. The y-intercept is -5.
Correct Answer:
D
— -2
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Q. What is the y-intercept of the line represented by the equation 4x - y + 8 = 0? (2019)
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Solution
Setting x = 0 in the equation gives -y + 8 = 0, thus y = 8.
Correct Answer:
A
— 8
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Q. Which of the following lines is parallel to the line 3x - 4y + 5 = 0?
A.
6x - 8y + 10 = 0
B.
4x + 3y - 7 = 0
C.
3x + 4y - 5 = 0
D.
2x - 3y + 1 = 0
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Solution
Parallel lines have the same slope. The slope of the given line is 3/4, and the line 6x - 8y + 10 = 0 also has the same slope.
Correct Answer:
A
— 6x - 8y + 10 = 0
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Q. Which of the following points lies on the parabola y = x^2 - 4?
A.
(2, 0)
B.
(0, -4)
C.
(1, -3)
D.
(3, 5)
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Solution
Substituting x = 1 into the equation gives y = 1^2 - 4 = -3, so the point (1, -3) lies on the parabola.
Correct Answer:
C
— (1, -3)
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Q. Which of the following points lies on the parabola y^2 = 8x?
A.
(2, 4)
B.
(1, 2)
C.
(4, 4)
D.
(2, 2)
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Solution
To check if a point lies on the parabola, substitute the x-coordinate into the equation. For (2, 4), 4^2 = 16 and 8*2 = 16, so it lies on the parabola.
Correct Answer:
A
— (2, 4)
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