Graph y=x^2+1

Graph y=x^2+1
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 .
Add and .
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 .
Add and .
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.
Add and .
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 .
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 thirteen million five hundred twenty-five thousand nine hundred twenty-four

Interesting facts

  • 213525924 has 32 divisors, whose sum is 640923840
  • The reverse of 213525924 is 429525312
  • Previous prime number is 7109

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 33
  • Digital Root 6

Name

Name one billion eight hundred sixty-two million nine hundred four thousand five hundred ninety-one

Interesting facts

  • 1862904591 has 16 divisors, whose sum is 3506644224
  • The reverse of 1862904591 is 1954092681
  • Previous prime number is 17

Basic properties

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

Name

Name one billion nine hundred seventy-seven million one hundred sixty thousand seven hundred forty-three

Interesting facts

  • 1977160743 has 4 divisors, whose sum is 2196845280
  • The reverse of 1977160743 is 3470617791
  • Previous prime number is 9

Basic properties

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