# Graph y=x^2+2x-2

Graph y=x^2+2x-2
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 .
Cancel the common factor.
Rewrite the expression.
Find the value of using the formula .
Simplify each term.
Raise to the power of .
Multiply by .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from .
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.
Simplify each term.
Raise to the power of .
Multiply by .
Simplify by subtracting numbers.
Subtract from .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Raise to the power of .
Multiply by .
Simplify by subtracting numbers.
Subtract from .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Raising to any positive power yields .
Multiply by .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
One to any power is one.
Multiply by .
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:
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### Name

Name one billion seven hundred ninety-three million three hundred five thousand three hundred twenty-nine

### Interesting facts

• 1793305329 has 16 divisors, whose sum is 2598113280
• The reverse of 1793305329 is 9235033971
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 42
• Digital Root 6

### Name

Name three hundred forty-one million five hundred twenty thousand nine hundred eighty-nine

### Interesting facts

• 341520989 has 4 divisors, whose sum is 350751324
• The reverse of 341520989 is 989025143
• Previous prime number is 37

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 41
• Digital Root 5

### Name

Name one billion seven hundred twenty-one million seven hundred fifty thousand five hundred eighty-three

### Interesting facts

• 1721750583 has 16 divisors, whose sum is 2054524416
• The reverse of 1721750583 is 3850571271
• Previous prime number is 23

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 39
• Digital Root 3