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Completing the Square
Main Concept
Completing the square is the name of a process used to convert quadratic polynomials in the general form to the vertex form:
where
,
Steps:
1. Factor the leading coefficient out of the first two terms
2. Complete the square by adding and subtracting the "magic number"
(the square of half the coefficient of )
3. Move the constant outside the parentheses. Remember to multiply it by a.
4. Factor the perfect square and add the remaining terms.
Numerical Example:
(the square of half the coefficient of x)
3. Move the constant outside the parentheses. Remember to multiply it by 3.
Click on "Next Step" to follow the steps of completing the square. Click on "New Quadratic" to start from a different polynomial. Observe that the magic number is the square of half the coefficient of x.
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