Find the Standard Form of the Parabola y=-(x-3)^2+11

$y = - {(x - 3)}^{2} + 11$

Step 1

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

$- {(x - 3)}^{2} + 11 = y$

Step 2

Subtract $11$ from both sides of the equation.

$- {(x - 3)}^{2} = y - 11$

Step 3

Divide each term in $- {(x - 3)}^{2} = y - 11$ by $- 1$ and simplify.

Divide each term in $- {(x - 3)}^{2} = y - 11$ by $- 1$ .

$\frac{- {(x - 3)}^{2}}{- 1} = \frac{y}{- 1} + \frac{- 11}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{{(x - 3)}^{2}}{1} = \frac{y}{- 1} + \frac{- 11}{- 1}$

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

${(x - 3)}^{2} = \frac{y}{- 1} + \frac{- 11}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{y}{- 1}$ .

${(x - 3)}^{2} = - 1 \cdot y + \frac{- 11}{- 1}$

Rewrite $- 1 \cdot y$ as $- y$ .

${(x - 3)}^{2} = - y + \frac{- 11}{- 1}$

Divide $- 11$ by $- 1$ .

${(x - 3)}^{2} = - y + 11$

Step 4

Factor.

Factor $- 1$ out of $- y$ .

${(x - 3)}^{2} = - (y) + 11$

Rewrite $11$ as $- 1 (- 11)$ .

${(x - 3)}^{2} = - (y) - 1 (- 11)$

Factor $- 1$ out of $- (y) - 1 (- 11)$ .

${(x - 3)}^{2} = - (y - 11)$