Find the Standard Form of the Parabola

$f (x) = 3 {(x - 2)}^{2} + 4$

Step 1

Write $f (x) = 3 {(x - 2)}^{2} + 4$ as an equation.

$y = 3 {(x - 2)}^{2} + 4$

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.

$3 {(x - 2)}^{2} + 4 = y$

Step 3

Subtract $4$ from both sides of the equation.

$3 {(x - 2)}^{2} = y - 4$

Step 4

Divide each term in $3 {(x - 2)}^{2} = y - 4$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 {(x - 2)}^{2} = y - 4$ by $3$ .

$\frac{3 {(x - 2)}^{2}}{3} = \frac{y}{3} + \frac{- 4}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 {(x - 2)}^{2}}{3} = \frac{y}{3} + \frac{- 4}{3}$

Step 4.2.1.2

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

${(x - 2)}^{2} = \frac{y}{3} + \frac{- 4}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

${(x - 2)}^{2} = \frac{y}{3} - \frac{4}{3}$

Step 5

Factor.

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Step 5.1

Combine the numerators over the common denominator.

${(x - 2)}^{2} = \frac{y - 4}{3}$

Step 5.2

Reorder terms.

${(x - 2)}^{2} = \frac{1}{3} (y - 4)$

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