Graph y=x^2-2

Graph y=x^2-2
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 .
Subtract from .
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 .
Subtract from .
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.
Subtract from .
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 .
Subtract from .
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 four hundred five million nine hundred seventy-five thousand eight hundred seventy-four

Interesting facts

  • 405975874 has 8 divisors, whose sum is 611131788
  • The reverse of 405975874 is 478579504
  • Previous prime number is 281

Basic properties

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

Name

Name eighty-six million six hundred sixty-one thousand eight hundred eighty

Interesting facts

  • 86661880 has 32 divisors, whose sum is 350980776
  • The reverse of 86661880 is 08816668
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 8
  • Sum of Digits 43
  • Digital Root 7

Name

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

Interesting facts

  • 2129516875 has 32 divisors, whose sum is 3192696000
  • The reverse of 2129516875 is 5786159212
  • Previous prime number is 2273

Basic properties

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