Find the Standard Form of the Parabola f(x)=5(x-1)^2-5

$f (x) = 5 {(x - 1)}^{2} - 5$

Step 1

Write $f (x) = 5 {(x - 1)}^{2} - 5$ as an equation.

$y = 5 {(x - 1)}^{2} - 5$

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.

$5 {(x - 1)}^{2} - 5 = y$

Step 3

Add $5$ to both sides of the equation.

$5 {(x - 1)}^{2} = y + 5$

Step 4

Divide each term in $5 {(x - 1)}^{2} = y + 5$ by $5$ and simplify.

Divide each term in $5 {(x - 1)}^{2} = y + 5$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $5$ by $5$ .

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

Step 5

Factor.

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

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

Combine the numerators over the common denominator.

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

Reorder terms.

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