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 eight hundred twenty-nine million eight hundred fourteen thousand two hundred sixty-four

Interesting facts

  • 829814264 has 16 divisors, whose sum is 2800623168
  • The reverse of 829814264 is 462418928
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 44
  • Digital Root 8

Name

Name six hundred sixty-eight million seven hundred forty-five thousand two

Interesting facts

  • 668745002 has 4 divisors, whose sum is 1003117506
  • The reverse of 668745002 is 200547866
  • Previous prime number is 2

Basic properties

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

Name

Name ninety-three million twenty-four thousand fifty-two

Interesting facts

  • 93024052 has 32 divisors, whose sum is 238261824
  • The reverse of 93024052 is 25042039
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 8
  • Sum of Digits 25
  • Digital Root 7