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

$f (x) = 2 x^{2}$

Step 1

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

$y = 2 x^{2}$

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.

$2 x^{2} = y$

Step 3

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 $1$ .

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

Step 4

Reorder terms.

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