Graph y=-2x^2

Graph y=-2x^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 .
Simplify the right side.
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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.
Cancel the common factor of and .
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Factor out of .
Move the negative one from the denominator of .
Simplify the expression.
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Rewrite as .
Multiply 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 negative, the parabola opens down.
Opens Down
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.
Simplify.
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Multiply by .
Move the negative in front of the fraction.
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 Down
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Down
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 .
Multiply by .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Multiply by by adding the exponents.
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Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
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.
Multiply by .
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 .
Multiply by .
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 Down
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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Name

Name one billion nine hundred fifty-four million five hundred seventy-three thousand three hundred four

Interesting facts

  • 1954573304 has 32 divisors, whose sum is 6883497936
  • The reverse of 1954573304 is 4033754591
  • Previous prime number is 23

Basic properties

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

Name

Name one billion three hundred twenty-two million five hundred seventy-nine thousand six hundred ninety-one

Interesting facts

  • 1322579691 has 16 divisors, whose sum is 1423392768
  • The reverse of 1322579691 is 1969752231
  • Previous prime number is 191

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 45
  • Digital Root 9

Name

Name one billion nine hundred fifty million six hundred thirty-nine thousand twelve

Interesting facts

  • 1950639012 has 32 divisors, whose sum is 4461848064
  • The reverse of 1950639012 is 2109360591
  • Previous prime number is 3251

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 36
  • Digital Root 9