Find the Axis of Symmetry y-4x=7-x^2

Find the Axis of Symmetry y-4x=7-x^2
Rewrite the equation in vertex form.
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Add to both sides of the equation.
Complete the square for .
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Move .
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 .
Move the negative one from the denominator of .
Multiply by .
Find the value of using the formula .
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Simplify each term.
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Cancel the common factor of and .
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Factor out of .
Move the negative one from the denominator of .
Multiply 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.
Cancel the common factor of and .
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Rewrite as .
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.
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Name

Name seven hundred thirty-three million forty-eight thousand sixty-four

Interesting facts

  • 733048064 has 2048 divisors, whose sum is 21646891008
  • The reverse of 733048064 is 460840337
  • Previous prime number is 127

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 35
  • Digital Root 8

Name

Name one billion five hundred sixty million eight hundred seventeen thousand five hundred thirty-six

Interesting facts

  • 1560817536 has 2048 divisors, whose sum is 37589806080
  • The reverse of 1560817536 is 6357180651
  • Previous prime number is 79

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name four hundred thirty-six million nine hundred eighty-seven thousand five hundred two

Interesting facts

  • 436987502 has 8 divisors, whose sum is 749121456
  • The reverse of 436987502 is 205789634
  • Previous prime number is 7

Basic properties

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