Graph y=x^2

Graph y=x^2
Find the properties of the given parabola.
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Rewrite the equation in vertex form.
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Complete the square for .
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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 .
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Factor out of .
Cancel the common factors.
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Cancel the common factor.
Rewrite the expression.
Divide by .
Find the value of using the formula .
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Simplify each term.
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Raising to any positive power yields .
Multiply by .
Divide by .
Multiply by .
Add and .
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.
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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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Raise to the power of .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Raise to the power of .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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One to any power is one.
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Raise to the power of .
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 one billion thirty-eight million seven hundred nineteen thousand sixty-six

Interesting facts

  • 1038719066 has 16 divisors, whose sum is 1600560000
  • The reverse of 1038719066 is 6609178301
  • Previous prime number is 71

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 41
  • Digital Root 5

Name

Name one billion eight hundred seventeen million forty-five thousand nine hundred forty-four

Interesting facts

  • 1817045944 has 64 divisors, whose sum is 7157735424
  • The reverse of 1817045944 is 4495407181
  • Previous prime number is 47

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7

Name

Name nine hundred seventy-five million six hundred twenty-two thousand six hundred forty-eight

Interesting facts

  • 975622648 has 128 divisors, whose sum is 3954935808
  • The reverse of 975622648 is 846226579
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 49
  • Digital Root 4