What is the axis of symmetry for the parabola defined by the equation y^2 = -12x

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Question: What is the axis of symmetry for the parabola defined by the equation y^2 = -12x?

Options:

Correct Answer: x = 0

Solution:

The axis of symmetry for a parabola in the form y^2 = 4px is the x-axis, which is x = 0.

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?

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.

Parabola Orientation – Understanding the orientation of parabolas defined by equations in the form y^2 = 4px, which opens to the left or right depending on the sign of p.
Axis of Symmetry – Identifying the axis of symmetry for parabolas, which is a vertical line for parabolas that open left or right.