Precalculus Examples

Consider the vertex form of the parabola.
Rewrite the function in terms of and .
Complete the square on the right side of the equation.
Tap for more steps...
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Find the value of using the formula .
Tap for more steps...
Multiply by .
Multiply by .
Move the negative in front of the fraction.
Simplify .
Tap for more steps...
Multiply by .
Multiply by .
Find the value of using the formula .
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Raise to the power of .
Multiply by .
Move the negative in front of the fraction.
Simplify .
Tap for more steps...
Multiply by .
Multiply by .
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 .
Tap for more steps...
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Multiply by .
Add and .
Substitute the values of , , and into the vertex form .
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 the focus.
Tap for more steps...
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.
Tap for more steps...
Reduce the expression by cancelling the common factors.
Tap for more steps...
Rewrite as .
Multiply by .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Find the focus.
Tap for more steps...
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.
Tap for more steps...
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 Down
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Enter YOUR Problem
Mathway requires javascript and a modern browser.