Find the Standard Form of the Parabola y=-5(x-3)^2-9

$y = - 5 {(x - 3)}^{2} - 9$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 5 {(x - 3)}^{2} - 9 = y$

Add $9$ to both sides of the equation.

$- 5 {(x - 3)}^{2} = y + 9$

Divide each term in $- 5 {(x - 3)}^{2} = y + 9$ by $- 5$ and simplify.

Divide each term in $- 5 {(x - 3)}^{2} = y + 9$ by $- 5$ .

$\frac{- 5 {(x - 3)}^{2}}{- 5} = \frac{y}{- 5} + \frac{9}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 {(x - 3)}^{2}}{- 5} = \frac{y}{- 5} + \frac{9}{- 5}$

Divide ${(x - 3)}^{2}$ by $1$ .

${(x - 3)}^{2} = \frac{y}{- 5} + \frac{9}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

${(x - 3)}^{2} = - \frac{y}{5} + \frac{9}{- 5}$

Move the negative in front of the fraction.

${(x - 3)}^{2} = - \frac{y}{5} - \frac{9}{5}$

Factor.

Factor $- 1$ out of $- \frac{y}{5} - \frac{9}{5}$ .

Factor $- 1$ out of $- \frac{y}{5}$ .

${(x - 3)}^{2} = - (\frac{y}{5}) - \frac{9}{5}$

Factor $- 1$ out of $- \frac{9}{5}$ .

${(x - 3)}^{2} = - (\frac{y}{5}) - (\frac{9}{5})$

Factor $- 1$ out of $- (\frac{y}{5}) - (\frac{9}{5})$ .

${(x - 3)}^{2} = - (\frac{y}{5} + \frac{9}{5})$

Combine the numerators over the common denominator.

${(x - 3)}^{2} = - \frac{y + 9}{5}$

Reorder terms.

${(x - 3)}^{2} = - (\frac{1}{5} (y + 9))$

Remove parentheses.

${(x - 3)}^{2} = - \frac{1}{5} (y + 9)$