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

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.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Multiply by .

Find the value of using the formula .

Simplify each term.

Cancel the common factor of and .

Rewrite as .

Apply the product rule to .

Raise to the power of .

Multiply by .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Subtract from .

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 .

Since the value of is positive, the parabola opens up.

Opens Up

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.

Multiply by .

The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.

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

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

Find the Axis of Symmetry f(x)=2x^2-4x-7