Graph y^2=3x+7

Graph y^2=3x+7
Rewrite the equation as .
Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
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.
Multiply the numerator by the reciprocal of the denominator.
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 .
Combine and .
Multiply the numerator by the reciprocal of the denominator.
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 positive, the parabola opens right.
Opens Right
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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Combine and .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Find the focus.
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The focus of a parabola can be found by adding to the x-coordinate if the parabola opens left or right.
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 vertical line found by subtracting from the x-coordinate of the vertex if the parabola opens left or right.
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 Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Right
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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Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Multiply by .
Add and .
The final answer is .
Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Multiply by .
Add and .
The final answer is .
Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Multiply by .
Add and .
The final answer is .
Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Multiply by .
Add and .
The final answer is .
Graph the parabola using its properties and the selected points.
Graph the parabola using its properties and the selected points.
Direction: Opens Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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Name

Name five hundred eighty-one million three hundred seventy-five thousand nine hundred forty-two

Interesting facts

  • 581375942 has 32 divisors, whose sum is 1013030400
  • The reverse of 581375942 is 249573185
  • Previous prime number is 73

Basic properties

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

Name

Name one hundred six million one hundred seventy-three thousand four hundred eleven

Interesting facts

  • 106173411 has 8 divisors, whose sum is 141705984
  • The reverse of 106173411 is 114371601
  • Previous prime number is 1031

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 24
  • Digital Root 6

Name

Name five hundred four million five hundred seventeen thousand seven hundred six

Interesting facts

  • 504517706 has 32 divisors, whose sum is 961331328
  • The reverse of 504517706 is 607715405
  • Previous prime number is 53

Basic properties

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