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What is the axis of symmetry for the parabola defined by the equation y^2 = -12x
What is the axis of symmetry for the parabola defined by the equation y^2 = -12x?
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Practice Questions
1 question
Q1
What is the axis of symmetry for the parabola defined by the equation y^2 = -12x?
x = 0
y = 0
y = -6
x = -6
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The axis of symmetry for a parabola in the form y^2 = 4px is the x-axis, which is x = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the axis of symmetry for the parabola defined by the equation y^2 = -12x?
Solution:
The axis of symmetry for a parabola in the form y^2 = 4px is the x-axis, which is x = 0.
Steps: 6
Show Steps
Step 1: Identify the form of the equation. The given equation is y^2 = -12x.
Step 2: Recognize that this equation is in the form y^2 = 4px, where p is a constant.
Step 3: Compare the equation y^2 = -12x with y^2 = 4px. Here, -12 can be written as 4p.
Step 4: Solve for p by setting 4p = -12. This gives p = -3.
Step 5: Understand that for parabolas in the form y^2 = 4px, the axis of symmetry is the line x = 0 (the y-axis).
Step 6: Conclude that the axis of symmetry for the given parabola is x = 0.
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