Find the Standard Form of the Parabola y+3=5(x-6)^2

$y + 3 = 5 {(x - 6)}^{2}$

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.

$5 {(x - 6)}^{2} = y + 3$

Step 2

Divide each term in $5 {(x - 6)}^{2} = y + 3$ by $5$ and simplify.

Divide each term in $5 {(x - 6)}^{2} = y + 3$ by $5$ .

$\frac{5 {(x - 6)}^{2}}{5} = \frac{y}{5} + \frac{3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 {(x - 6)}^{2}}{5} = \frac{y}{5} + \frac{3}{5}$

Divide ${(x - 6)}^{2}$ by $1$ .

${(x - 6)}^{2} = \frac{y}{5} + \frac{3}{5}$

Step 3

Factor.

Combine the numerators over the common denominator.

${(x - 6)}^{2} = \frac{y + 3}{5}$

Reorder terms.

${(x - 6)}^{2} = \frac{1}{5} (y + 3)$