Find the Standard Form of the Parabola y=5(x+1/5)^2-26/5

$y = 5 {(x + \frac{1}{5})}^{2} - \frac{26}{5}$

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

$5 {(x + \frac{1}{5})}^{2} - \frac{26}{5} = y$

Add $\frac{26}{5}$ to both sides of the equation.

$5 {(x + \frac{1}{5})}^{2} = y + \frac{26}{5}$

Divide each term in $5 {(x + \frac{1}{5})}^{2} = y + \frac{26}{5}$ by $5$ and simplify.

Divide each term in $5 {(x + \frac{1}{5})}^{2} = y + \frac{26}{5}$ by $5$ .

$\frac{5 {(x + \frac{1}{5})}^{2}}{5} = \frac{y}{5} + \frac{\frac{26}{5}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 {(x + \frac{1}{5})}^{2}}{5} = \frac{y}{5} + \frac{\frac{26}{5}}{5}$

Divide ${(x + \frac{1}{5})}^{2}$ by $1$ .

${(x + \frac{1}{5})}^{2} = \frac{y}{5} + \frac{\frac{26}{5}}{5}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

${(x + \frac{1}{5})}^{2} = \frac{y}{5} + \frac{26}{5} \cdot \frac{1}{5}$

Multiply $\frac{26}{5} \cdot \frac{1}{5}$ .

Multiply $\frac{26}{5}$ by $\frac{1}{5}$ .

${(x + \frac{1}{5})}^{2} = \frac{y}{5} + \frac{26}{5 \cdot 5}$

Multiply $5$ by $5$ .

${(x + \frac{1}{5})}^{2} = \frac{y}{5} + \frac{26}{25}$

Factor.

To write $\frac{y}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

${(x + \frac{1}{5})}^{2} = \frac{y}{5} \cdot \frac{5}{5} + \frac{26}{25}$

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y}{5}$ by $\frac{5}{5}$ .

${(x + \frac{1}{5})}^{2} = \frac{y \cdot 5}{5 \cdot 5} + \frac{26}{25}$

Multiply $5$ by $5$ .

${(x + \frac{1}{5})}^{2} = \frac{y \cdot 5}{25} + \frac{26}{25}$

Combine the numerators over the common denominator.

${(x + \frac{1}{5})}^{2} = \frac{y \cdot 5 + 26}{25}$

Move $5$ to the left of $y$ .

${(x + \frac{1}{5})}^{2} = \frac{5 y + 26}{25}$

Reorder terms.

${(x + \frac{1}{5})}^{2} = \frac{1}{25} (5 y + 26)$