Find the Standard Form of the Parabola y=2(x+4)^2-7

$y = 2 {(x + 4)}^{2} - 7$

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.

$2 {(x + 4)}^{2} - 7 = y$

Step 2

Add $7$ to both sides of the equation.

$2 {(x + 4)}^{2} = y + 7$

Step 3

Divide each term in $2 {(x + 4)}^{2} = y + 7$ by $2$ and simplify.

Divide each term in $2 {(x + 4)}^{2} = y + 7$ by $2$ .

$\frac{2 {(x + 4)}^{2}}{2} = \frac{y}{2} + \frac{7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x + 4)}^{2}}{2} = \frac{y}{2} + \frac{7}{2}$

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

${(x + 4)}^{2} = \frac{y}{2} + \frac{7}{2}$

Step 4

Factor.

Combine the numerators over the common denominator.

${(x + 4)}^{2} = \frac{y + 7}{2}$

Reorder terms.

${(x + 4)}^{2} = \frac{1}{2} (y + 7)$