# Graph y=x^2-4

Graph y=x^2-4
Find the properties of the given parabola.
Rewrite the equation in vertex form.
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 .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
Divide by .
Find the value of using the formula .
Simplify each term.
Raising to any positive power yields .
Multiply by .
Divide by .
Multiply by .
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.
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 .
Cancel the common factor.
Rewrite the expression.
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:
Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.
Replace the variable with in the expression.
Simplify the result.
Raise to the power of .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Raise to the power of .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
One to any power is one.
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Raise to the power of .
Subtract from .
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:
Do you know how to Graph y=x^2-4? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

### Name

Name two hundred thirty-seven million nine hundred sixty-seven thousand one hundred twenty-six

### Interesting facts

• 237967126 has 8 divisors, whose sum is 357548400
• The reverse of 237967126 is 621769732
• Previous prime number is 599

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 43
• Digital Root 7

### Name

Name one billion one hundred sixty-four million two hundred fifty-one thousand seven hundred twenty-seven

### Interesting facts

• 1164251727 has 8 divisors, whose sum is 1293843280
• The reverse of 1164251727 is 7271524611
• Previous prime number is 9733

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 36
• Digital Root 9

### Name

Name one billion four hundred three million one hundred forty thousand five hundred thirteen

### Interesting facts

• 1403140513 has 4 divisors, whose sum is 1411542720
• The reverse of 1403140513 is 3150413041
• Previous prime number is 167

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 22
• Digital Root 4