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 the focus.

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.

Combine and .

Divide by .

Find the focus.

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 directrix.

The directrix of a parabola is the horizontal line found by subtracting from the y-coordinate of the vertex if the parabola opens up or down.

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

Use the properties of the parabola to analyze and graph the parabola.

Direction: Opens Up

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Direction: Opens Up

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

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 .

Simplify by adding and subtracting.

Subtract from .

Add and .

The final answer is .

The value at is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raise to the power of .

Multiply by .

Find the common denominator.

Write as a fraction with denominator .

Multiply by .

Multiply and .

Write as a fraction with denominator .

Multiply by .

Multiply and .

Combine the numerators over the common denominator.

Simplify each term.

Multiply by .

Multiply by .

Simplify the expression.

Subtract from .

Add and .

Move the negative in front of the fraction.

The final answer is .

The value at is .

Replace the variable with in the expression.

Simplify the result.

Find the common denominator.

Write as a fraction with denominator .

Multiply by .

Multiply and .

Write as a fraction with denominator .

Multiply by .

Multiply and .

Combine the numerators over the common denominator.

Simplify each term.

Raise to the power of .

Multiply by .

Multiply by .

Multiply by .

Simplify the expression.

Subtract from .

Add and .

Divide by .

The final answer is .

The value at is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raise to the power of .

Multiply by .

Find the common denominator.

Write as a fraction with denominator .

Multiply by .

Multiply and .

Write as a fraction with denominator .

Multiply by .

Multiply and .

Combine the numerators over the common denominator.

Simplify each term.

Multiply by .

Multiply by .

Simplify the expression.

Subtract from .

Add and .

Move the negative in front of the fraction.

The final answer is .

The value at is .

Graph the parabola using its properties and the selected points.

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Graph y=1/2*(x-4)^2-2