Find the Standard Form of the Parabola f(x)=-3(2-x)^2

$f (x) = - 3 {(2 - x)}^{2}$

Step 1

Write $f (x) = - 3 {(2 - x)}^{2}$ as an equation.

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

Step 2

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

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

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 4

Factor.

Reorder terms.

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

Remove parentheses.

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