Completing the Square - Maple Programming Help

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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 $x$) $=$ 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:

 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 x) $=$ 3. Move the constant $-1$ outside the parentheses. Remember to multiply it by 3. $=$ 4. Factor the perfect square and add the remaining terms. $=$

Click "Next Step" to follow the steps of completing the square. Click "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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