# Precalculus Examples

Consider the vertex form of the parabola.

Rewrite the function in terms of and .

Use the form , to find the values of , , and .

Consider the vertex form of a parabola.

Find the value of using the formula .

Multiply by to get .

Multiply by to get .

Find the value of using the formula .

Simplify each term.

Multiply by to get .

Simplify the numerator.

Remove parentheses around .

Raise to the power of to get .

Simplify the denominator.

Remove parentheses.

Multiply by to get .

Multiply by to get .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Multiply by to get .

Subtract from to get .

Move the negative in front of the fraction.

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

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 to get .

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.

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: