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.

Multiply by .

Move the negative in front of the fraction.

Find the value of using the formula .

Simplify each term.

Raise to the power of .

Multiply by .

Move the negative in front of the fraction.

Multiply .

Multiply by .

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 .

Add and .

Move the negative in front of the fraction.

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 negative, the parabola opens down.

Opens Down

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.

Multiply by .

Move the negative in front of the fraction.

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 y=-2x^2+3x-4