Find the Vertex Form 6(x-2)^2+3y=3

$6 {(x - 2)}^{2} + 3 y = 3$

Step 1

Subtract $6 {(x - 2)}^{2}$ from both sides of the equation.

$3 y = 3 - 6 {(x - 2)}^{2}$

Step 2

Divide each term in $3 y = 3 - 6 {(x - 2)}^{2}$ by $3$ and simplify.

Divide each term in $3 y = 3 - 6 {(x - 2)}^{2}$ by $3$ .

$\frac{3 y}{3} = \frac{3}{3} + \frac{- 6 {(x - 2)}^{2}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{3}{3} + \frac{- 6 {(x - 2)}^{2}}{3}$

Divide $y$ by $1$ .

$y = \frac{3}{3} + \frac{- 6 {(x - 2)}^{2}}{3}$

Simplify the right side.

Simplify each term.

Divide $3$ by $3$ .

$y = 1 + \frac{- 6 {(x - 2)}^{2}}{3}$

Cancel the common factor of $- 6$ and $3$ .

Factor $3$ out of $- 6 {(x - 2)}^{2}$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 3

Reorder terms.

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