Graph y=(x+3)^2

Graph y=(x+3)^2
Find the properties of the given parabola.
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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.
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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 .
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Cancel the common factor.
Rewrite the expression.
Find the focus.
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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.
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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.
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
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Subtract from .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
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Subtract from .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
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Subtract from .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
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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 eighty-two million eight hundred thousand three hundred ninety-eight

Interesting facts

  • 282800398 has 8 divisors, whose sum is 435665592
  • The reverse of 282800398 is 893008282
  • Previous prime number is 37

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 40
  • Digital Root 4

Name

Name one billion eight hundred sixty-six million eight hundred forty-six thousand sixteen

Interesting facts

  • 1866846016 has 512 divisors, whose sum is 24819685632
  • The reverse of 1866846016 is 6106486681
  • Previous prime number is 47

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 46
  • Digital Root 1

Name

Name eight hundred sixteen million nine hundred eighty-nine thousand seven hundred twenty-eight

Interesting facts

  • 816989728 has 128 divisors, whose sum is 6245138880
  • The reverse of 816989728 is 827989618
  • Previous prime number is 151

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 58
  • Digital Root 4