Write as a Function of x x=-8y^2

$x = - 8 y^{2}$

Step 1

Rewrite the equation as $- 8 y^{2} = x$ .

$- 8 y^{2} = x$

Step 2

Divide each term in $- 8 y^{2} = x$ by $- 8$ and simplify.

Divide each term in $- 8 y^{2} = x$ by $- 8$ .

$\frac{- 8 y^{2}}{- 8} = \frac{x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y^{2}}{- 8} = \frac{x}{- 8}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{x}{- 8}$

Simplify the right side.

Move the negative in front of the fraction.

$y^{2} = - \frac{x}{8}$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{- \frac{x}{8}}$

Step 4

Simplify $\pm \sqrt{- \frac{x}{8}}$ .

Rewrite $- \frac{x}{8}$ as ${(\frac{1^{2}}{2})}^{2} \cdot (- \frac{x}{2})$ .

Factor the perfect power $1^{2}$ out of $x$ .

$y = \pm \sqrt{- \frac{1^{2} x}{8}}$

Factor the perfect power $2^{2}$ out of $8$ .

$y = \pm \sqrt{- \frac{1^{2} x}{2^{2} \cdot 2}}$

Rearrange the fraction $\frac{1^{2} x}{2^{2} \cdot 2}$ .

$y = \pm \sqrt{- ({(\frac{1}{2})}^{2} \frac{x}{2})}$

Reorder $- 1$ and ${(\frac{1}{2})}^{2}$ .

$y = \pm \sqrt{{(\frac{1}{2})}^{2} \cdot - 1 \frac{x}{2}}$

Rewrite $1$ as $1^{2}$ .

$y = \pm \sqrt{{(\frac{1^{2}}{2})}^{2} \cdot - 1 \frac{x}{2}}$

Add parentheses.

$y = \pm \sqrt{{(\frac{1^{2}}{2})}^{2} \cdot (- \frac{x}{2})}$

Pull terms out from under the radical.

$y = \pm \frac{1^{2}}{2} \sqrt{- \frac{x}{2}}$

One to any power is one.

$y = \pm \frac{1}{2} \sqrt{- \frac{x}{2}}$

Combine $\frac{1}{2}$ and $\sqrt{- \frac{x}{2}}$ .

$y = \pm \frac{\sqrt{- \frac{x}{2}}}{2}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \frac{\sqrt{- \frac{x}{2}}}{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \frac{\sqrt{- \frac{x}{2}}}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{\sqrt{- \frac{x}{2}}}{2}$

$y = - \frac{\sqrt{- \frac{x}{2}}}{2}$

$y = \frac{\sqrt{- \frac{x}{2}}}{2}$

$y = - \frac{\sqrt{- \frac{x}{2}}}{2}$

Step 6

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \frac{\sqrt{- \frac{x}{2}}}{2}, - \frac{\sqrt{- \frac{x}{2}}}{2}$

Write as a Function of x x=-8y^2

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