Find the Standard Form of the Parabola y=-37(x-82)^2-16

$y = - 37 {(x - 82)}^{2} - 16$

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.

$- 37 {(x - 82)}^{2} - 16 = y$

Step 2

Add $16$ to both sides of the equation.

$- 37 {(x - 82)}^{2} = y + 16$

Step 3

Divide each term in $- 37 {(x - 82)}^{2} = y + 16$ by $- 37$ and simplify.

Divide each term in $- 37 {(x - 82)}^{2} = y + 16$ by $- 37$ .

$\frac{- 37 {(x - 82)}^{2}}{- 37} = \frac{y}{- 37} + \frac{16}{- 37}$

Simplify the left side.

Cancel the common factor of $- 37$ .

Cancel the common factor.

$\frac{- 37 {(x - 82)}^{2}}{- 37} = \frac{y}{- 37} + \frac{16}{- 37}$

Divide ${(x - 82)}^{2}$ by $1$ .

${(x - 82)}^{2} = \frac{y}{- 37} + \frac{16}{- 37}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

${(x - 82)}^{2} = - \frac{y}{37} + \frac{16}{- 37}$

Move the negative in front of the fraction.

${(x - 82)}^{2} = - \frac{y}{37} - \frac{16}{37}$

Step 4

Factor.

Factor $- 1$ out of $- \frac{y}{37} - \frac{16}{37}$ .

Factor $- 1$ out of $- \frac{y}{37}$ .

${(x - 82)}^{2} = - (\frac{y}{37}) - \frac{16}{37}$

Factor $- 1$ out of $- \frac{16}{37}$ .

${(x - 82)}^{2} = - (\frac{y}{37}) - (\frac{16}{37})$

Factor $- 1$ out of $- (\frac{y}{37}) - (\frac{16}{37})$ .

${(x - 82)}^{2} = - (\frac{y}{37} + \frac{16}{37})$

Combine the numerators over the common denominator.

${(x - 82)}^{2} = - \frac{y + 16}{37}$

Reorder terms.

${(x - 82)}^{2} = - (\frac{1}{37} (y + 16))$

Remove parentheses.

${(x - 82)}^{2} = - \frac{1}{37} (y + 16)$