Pre-Algebra Examples

Graph 4x^2-24x+4y^2+4y-107=0
Step 1
Add to both sides of the equation.
Step 2
Divide both sides of the equation by .
Step 3
Complete the square for .
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Step 3.1
Use the form , to find the values of , , and .
Step 3.2
Consider the vertex form of a parabola.
Step 3.3
Find the value of using the formula .
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Step 3.3.1
Substitute the values of and into the formula .
Step 3.3.2
Cancel the common factor of and .
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Step 3.3.2.1
Factor out of .
Step 3.3.2.2
Cancel the common factors.
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Step 3.3.2.2.1
Factor out of .
Step 3.3.2.2.2
Cancel the common factor.
Step 3.3.2.2.3
Rewrite the expression.
Step 3.3.2.2.4
Divide by .
Step 3.4
Find the value of using the formula .
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Step 3.4.1
Substitute the values of , and into the formula .
Step 3.4.2
Simplify the right side.
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Step 3.4.2.1
Simplify each term.
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Step 3.4.2.1.1
Raise to the power of .
Step 3.4.2.1.2
Multiply by .
Step 3.4.2.1.3
Divide by .
Step 3.4.2.1.4
Multiply by .
Step 3.4.2.2
Subtract from .
Step 3.5
Substitute the values of , , and into the vertex form .
Step 4
Substitute for in the equation .
Step 5
Move to the right side of the equation by adding to both sides.
Step 6
Complete the square for .
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Step 6.1
Use the form , to find the values of , , and .
Step 6.2
Consider the vertex form of a parabola.
Step 6.3
Find the value of using the formula .
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Step 6.3.1
Substitute the values of and into the formula .
Step 6.3.2
Cancel the common factor of .
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Step 6.3.2.1
Cancel the common factor.
Step 6.3.2.2
Rewrite the expression.
Step 6.4
Find the value of using the formula .
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Step 6.4.1
Substitute the values of , and into the formula .
Step 6.4.2
Simplify the right side.
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Step 6.4.2.1
Simplify each term.
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Step 6.4.2.1.1
One to any power is one.
Step 6.4.2.1.2
Multiply by .
Step 6.4.2.2
Subtract from .
Step 6.5
Substitute the values of , , and into the vertex form .
Step 7
Substitute for in the equation .
Step 8
Move to the right side of the equation by adding to both sides.
Step 9
Simplify .
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Step 9.1
Combine the numerators over the common denominator.
Step 9.2
Simplify the expression.
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Step 9.2.1
Add and .
Step 9.2.2
Divide by .
Step 9.2.3
Add and .
Step 10
This is the form of a circle. Use this form to determine the center and radius of the circle.
Step 11
Match the values in this circle to those of the standard form. The variable represents the radius of the circle, represents the x-offset from the origin, and represents the y-offset from origin.
Step 12
The center of the circle is found at .
Center:
Step 13
These values represent the important values for graphing and analyzing a circle.
Center:
Radius:
Step 14