Find the Standard Form of the Parabola f(x)=3(x-1)^2-3

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

Step 1

Write $f (x) = 3 {(x - 1)}^{2} - 3$ as an equation.

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

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.

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

Step 3

Add $3$ to both sides of the equation.

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

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $3$ by $3$ .

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

Step 5

Factor.

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Reorder terms.

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