Set the polynomial equal to to find the properties of the parabola.

Combine and .

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.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply .

Multiply and .

Multiply by .

Find the value of using the formula .

Simplify each term.

Simplify the numerator.

Apply the product rule to .

One to any power is one.

Raise to the power of .

Multiply by .

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply and .

Multiply by .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

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

Set equal to the new right side.

Find the Vertex Form f(x)=2x^2+1/2x+8