Isolate to the left side of the equation.

Rewrite the equation as .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

Complete the square for .

Use the form , to find the values of , , and .

Consider the vertex form of a parabola.

Substitute the values of and into the formula .

Simplify the right side.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply by .

Find the value of using the formula .

Simplify each term.

Raising to any positive power yields .

Simplify the denominator.

Multiply by .

Combine and .

Reduce the expression by cancelling the common factors.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply by .

Multiply by .

Add and .

Substitute the values of , , and into the vertex form .

Set equal to the new right side.

Use the vertex form, , to determine the values of , , and .

Find the vertex .

Find the distance from the vertex to a focus of the parabola by using the following formula.

Substitute the value of into the formula.

Simplify.

Cancel the common factor of and .

Rewrite as .

Move the negative in front of the fraction.

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply by .

The directrix of a parabola is the vertical line found by subtracting from the x-coordinate of the vertex if the parabola opens left or right.

Substitute the known values of and into the formula and simplify.

Find the Directrix y^2=-32x