Find the Standard Form of the Parabola y=3(x-4)^2-22

$y = 3 {(x - 4)}^{2} - 22$

Step 1

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

$3 {(x - 4)}^{2} - 22 = y$

Step 2

Add $22$ to both sides of the equation.

$3 {(x - 4)}^{2} = y + 22$

Step 3

Divide each term in $3 {(x - 4)}^{2} = y + 22$ by $3$ and simplify.

Divide each term in $3 {(x - 4)}^{2} = y + 22$ by $3$ .

$\frac{3 {(x - 4)}^{2}}{3} = \frac{y}{3} + \frac{22}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(x - 4)}^{2}}{3} = \frac{y}{3} + \frac{22}{3}$

Divide ${(x - 4)}^{2}$ by $1$ .

${(x - 4)}^{2} = \frac{y}{3} + \frac{22}{3}$

Step 4

Factor.

Combine the numerators over the common denominator.

${(x - 4)}^{2} = \frac{y + 22}{3}$

Reorder terms.

${(x - 4)}^{2} = \frac{1}{3} (y + 22)$