Combine and .

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 .

Divide by .

Divide 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 .

Divide by .

The focus of a parabola can be found by adding to the x-coordinate if the parabola opens left or right.

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

Find the Focus x=-1/2y^2