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

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

Step 1

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

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

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.

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

Step 3

Subtract $1$ from both sides of the equation.

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

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide ${(x - 3)}^{2}$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

Factor.

Combine the numerators over the common denominator.

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

Reorder terms.

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