# Graph y=(x+3)^2

Graph y=(x+3)^2
Find the properties of the given parabola.
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 adding and subtracting.
Subtract from .
Add and .
The final answer is .
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 adding and subtracting.
Subtract from .
Add and .
The final answer is .
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 adding and subtracting.
Subtract from .
Add and .
The final answer is .
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 adding and subtracting.
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:
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### Name

Name two hundred twenty-five million eight hundred twenty-nine thousand one hundred seventy-nine

### Interesting facts

• 225829179 has 4 divisors, whose sum is 250921320
• The reverse of 225829179 is 971928522
• Previous prime number is 9

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 45
• Digital Root 9

### Name

Name nine hundred fifty million seven hundred thirty-seven thousand four hundred three

### Interesting facts

• 950737403 has 16 divisors, whose sum is 1186099200
• The reverse of 950737403 is 304737059
• Previous prime number is 2111

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 38
• Digital Root 2

### Name

Name one billion one hundred sixty-six million three hundred eighty-three thousand two hundred thirty-nine

### Interesting facts

• 1166383239 has 8 divisors, whose sum is 1777345920
• The reverse of 1166383239 is 9323836611
• Previous prime number is 7

### Basic properties

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