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Which of the following equations represents a parabola in the xy-plane with a vertex that lies on the x-axis?
- a)y = (x - 3)2 + 2
- b)y = 2(x - 3)2
- c)y = 2x2 - 3
- d)y = 3x2 + 2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following equations represents a parabola in the xy-plane...
The general equation of a parabola in the xy-plane is y = a(x - h)2 + k, in which (h, k) is the vertex. Now let's express each choice in precisely this form.
(A) y = (x - 3)2 + 2 y = 1(x - 3)2 + 2 a = 1, h = 3, k = 2
(B) y = 2(x - 3)2 y = 2(x - 3)2 + 0 a = 2, h = 3, k = 0
(C) y = 2x2 - 3 y = 2(x - 0)2 - 3 a = 2, h = 0, k = -3
(D) y = 3x2 + 2 y = 3(x - 0)2 + 2 a = 3, h = 0, k = 2
If this vertex is on the x-axis, then k = 0. The only equation in which k = 0 is (B).
(A) y = (x - 3)2 + 2 y = 1(x - 3)2 + 2 a = 1, h = 3, k = 2
(B) y = 2(x - 3)2 y = 2(x - 3)2 + 0 a = 2, h = 3, k = 0
(C) y = 2x2 - 3 y = 2(x - 0)2 - 3 a = 2, h = 0, k = -3
(D) y = 3x2 + 2 y = 3(x - 0)2 + 2 a = 3, h = 0, k = 2
If this vertex is on the x-axis, then k = 0. The only equation in which k = 0 is (B).
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Which of the following equations represents a parabola in the xy-plane...
Given:
The equation represents a parabola in the xy-plane with a vertex that lies on the x-axis.
To find:
Which of the following equations represents the given scenario.
Solution:
To determine which of the given equations represents a parabola in the xy-plane with a vertex on the x-axis, we need to analyze the general form of a parabolic equation.
The general equation of a parabola in the xy-plane is given by:
y = ax^2 + bx + c
The vertex form of a parabola is given by:
y = a(x - h)^2 + k
Where (h, k) represents the coordinates of the vertex.
Now, let's analyze each equation to determine which one fits the given scenario:
Option A: y = (x - 3)^2
In this equation, the vertex is located at (3, 0) since the x-coordinate of the vertex is 3 and the y-coordinate is 0. Therefore, this equation does not represent a parabola with a vertex on the x-axis.
Option B: y = 2(x - 3)^2
In this equation, the vertex is located at (3, 0) since the x-coordinate of the vertex is 3 and the y-coordinate is 0. Therefore, this equation represents a parabola with a vertex on the x-axis.
Option C: y = 2x^2 - 3
In this equation, the vertex does not lie on the x-axis since the y-coordinate of the vertex is -3. Therefore, this equation does not represent a parabola with a vertex on the x-axis.
Option D: y = 3x^2
In this equation, the vertex is located at the origin (0, 0) since both the x-coordinate and y-coordinate of the vertex are 0. Therefore, this equation does not represent a parabola with a vertex on the x-axis.
Conclusion:
Out of the given options, only option B represents a parabola in the xy-plane with a vertex that lies on the x-axis.
The equation represents a parabola in the xy-plane with a vertex that lies on the x-axis.
To find:
Which of the following equations represents the given scenario.
Solution:
To determine which of the given equations represents a parabola in the xy-plane with a vertex on the x-axis, we need to analyze the general form of a parabolic equation.
The general equation of a parabola in the xy-plane is given by:
y = ax^2 + bx + c
The vertex form of a parabola is given by:
y = a(x - h)^2 + k
Where (h, k) represents the coordinates of the vertex.
Now, let's analyze each equation to determine which one fits the given scenario:
Option A: y = (x - 3)^2
In this equation, the vertex is located at (3, 0) since the x-coordinate of the vertex is 3 and the y-coordinate is 0. Therefore, this equation does not represent a parabola with a vertex on the x-axis.
Option B: y = 2(x - 3)^2
In this equation, the vertex is located at (3, 0) since the x-coordinate of the vertex is 3 and the y-coordinate is 0. Therefore, this equation represents a parabola with a vertex on the x-axis.
Option C: y = 2x^2 - 3
In this equation, the vertex does not lie on the x-axis since the y-coordinate of the vertex is -3. Therefore, this equation does not represent a parabola with a vertex on the x-axis.
Option D: y = 3x^2
In this equation, the vertex is located at the origin (0, 0) since both the x-coordinate and y-coordinate of the vertex are 0. Therefore, this equation does not represent a parabola with a vertex on the x-axis.
Conclusion:
Out of the given options, only option B represents a parabola in the xy-plane with a vertex that lies on the x-axis.
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Which of the following equations represents a parabola in the xy-plane with a vertex that lies on the x-axis?a)y = (x - 3)2 + 2b)y = 2(x - 3)2c)y = 2x2 - 3d)y = 3x2 + 2Correct answer is option 'B'. Can you explain this answer?
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