What is the axis of symmetry of the parabola ?
Simplify any fractions.
J)

Question

What is the axis of symmetry of the parabola $$ x=-5 y^{2}-5 $$ ? Simplify any fractions. J)

UpStudy AI · Accepted Answer

The given equation of the parabola is:

$$
x = -5y^{2} - 5
$$

This is a horizontal parabola because the equation is solved for $$ x $$ in terms of $$ y^2 $$. To determine the axis of symmetry, observe the following:

1. **Symmetry Check**: Replace $$ y $$ with $$ -y $$ to check for symmetry.

$$
x = -5(-y)^{2} - 5 = -5y^{2} - 5
$$

Since the equation remains unchanged, the parabola is symmetric about a horizontal line.

2. **Axis of Symmetry**: The symmetry is about the line $$ y = 0 $$, which is the **x-axis**.

Therefore, the axis of symmetry for the parabola $$ x = -5y^{2} - 5 $$ is:

$$
\boxed{y=0}
$$
The axis of symmetry for the parabola $$ x = -5y^{2} - 5 $$ is $$ y = 0 $$.

What is the axis of symmetry of the parabola ?
Simplify any fractions.
J)

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What is the axis of symmetry of the parabola ? Simplify any fractions. J)

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What is the axis of symmetry of the parabola ?
Simplify any fractions.
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