Find the Standard Form of the Parabola y=-2x^2

$y = - 2 x^{2}$

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.

$- 2 x^{2} = y$

Step 2

Divide each term in $- 2 x^{2} = y$ by $- 2$ and simplify.

Divide each term in $- 2 x^{2} = y$ by $- 2$ .

$\frac{- 2 x^{2}}{- 2} = \frac{y}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x^{2}}{- 2} = \frac{y}{- 2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{y}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$x^{2} = - \frac{y}{2}$

Step 3

Factor.

Reorder terms.

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

Remove parentheses.

$x^{2} = - \frac{1}{2} y$