Write in Standard Form (y+5)^2=-1/3(x-3)

${(y + 5)}^{2} = - \frac{1}{3} (x - 3)$

Solve for $y$ .

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

$y + 5 = \pm \sqrt{- \frac{1}{3} \cdot (x - 3)}$

Reorder factors in $\pm \sqrt{- \frac{1}{3} \cdot (x - 3)}$ .

$y + 5 = \pm \sqrt{- (x - 3) \frac{1}{3}}$

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.

$y + 5 = \sqrt{- (x - 3) \frac{1}{3}}$

Subtract $5$ from both sides of the equation.

$y = \sqrt{- (x - 3) \frac{1}{3}} - 5$

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

$y + 5 = - \sqrt{- (x - 3) \frac{1}{3}}$

Subtract $5$ from both sides of the equation.