Calculus Examples

Find the properties of the given parabola.
Tap for more steps...
Rewrite the equation in vertex form.
Tap for more steps...
Complete the square for .
Tap for more steps...
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Multiply by .
Find the value of using the formula .
Tap for more steps...
Simplify each term.
Tap for more steps...
Raise to the power of .
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.
Tap for more steps...
Multiply by .
Subtract from .
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 positive, the parabola opens up.
Opens Up
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.
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Rewrite the expression.
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 Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.
Tap for more steps...
Replace the variable with in the expression.
Simplify the result.
Tap for more steps...
Simplify each term.
Tap for more steps...
One to any power is one.
Multiply by .
Simplify by adding and subtracting.
Tap for more steps...
Subtract from .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Tap for more steps...
Simplify each term.
Tap for more steps...
Raising to any positive power yields .
Multiply by .
Simplify by adding numbers.
Tap for more steps...
Add and .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Tap for more steps...
Simplify each term.
Tap for more steps...
Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
Tap for more steps...
Subtract from .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Tap for more steps...
Simplify each term.
Tap for more steps...
Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
Tap for more steps...
Subtract from .
Add and .
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:
Enter YOUR Problem
Mathway requires javascript and a modern browser.
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information