Find the Standard Form of the Parabola y=-(x-1)^2+25

$y = - {(x - 1)}^{2} + 25$

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

$- {(x - 1)}^{2} + 25 = y$

Subtract $25$ from both sides of the equation.

$- {(x - 1)}^{2} = y - 25$

Divide each term in $- {(x - 1)}^{2} = y - 25$ by $- 1$ and simplify.

Divide each term in $- {(x - 1)}^{2} = y - 25$ by $- 1$ .

$\frac{- {(x - 1)}^{2}}{- 1} = \frac{y}{- 1} + \frac{- 25}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{{(x - 1)}^{2}}{1} = \frac{y}{- 1} + \frac{- 25}{- 1}$

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

${(x - 1)}^{2} = \frac{y}{- 1} + \frac{- 25}{- 1}$

Simplify the right side.

Simplify each term.

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

${(x - 1)}^{2} = - 1 \cdot y + \frac{- 25}{- 1}$

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

${(x - 1)}^{2} = - y + \frac{- 25}{- 1}$

Divide $- 25$ by $- 1$ .

${(x - 1)}^{2} = - y + 25$

Factor.

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

${(x - 1)}^{2} = - (y) + 25$

Rewrite $25$ as $- 1 (- 25)$ .

${(x - 1)}^{2} = - (y) - 1 (- 25)$

Factor $- 1$ out of $- (y) - 1 (- 25)$ .

${(x - 1)}^{2} = - (y - 25)$