transform quadratic expressions to completed square form - Maple Help

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Student[Precalculus][CompleteSquare] - transform quadratic expressions to completed square form

Calling Sequence

CompleteSquare(f, x, ...)

Parameters

f

-

algebraic expression, equation, or an inequality involving algebraic terms

x

-

(optional) name, function, list, or set

...

-

(optional) name or function

Description

• 

The CompleteSquare(f, x) command, where f is a quadratic expression, equation, or an inequality in x, completes the square of f.  If f is not itself quadratic in x, its subexpressions are examined, and any which are quadratic in x are transformed to completed square form.

• 

If x is a list or set, the operation of completing the square is applied successively to each component of x.  These components can be names, such as u and v, or functions, such as sint and ⅆⅆwhw.

• 

The CompleteSquare(f) command is equivalent to CompleteSquare(f, indets(f,name)).

• 

The command CompleteSquare(f, [x, y]) is equivalent to the command CompleteSquare(f, x, y).

• 

The completed square form of the general quadratic expression ax2+bx+c is ax+12ba2+c14b2a.

Examples

withStudent[Precalculus]:

CompleteSquare3x2+2x,x

3x+13213

(1)

CompleteSquarex21y3+2y2xy,x

1y3x+y21y32yy41y3

(2)

CompleteSquare1sint2+2sint+1,sint

1sint+12

(3)

CompleteSquarea2+b2+a+b,a,b

b+122+a+12212

(4)

CompleteSquarex2x=y2+2y+3

x12214=y+12+2

(5)

CompleteSquare∫∫u2+2uv23vⅆvⅆu,u,v

∫∫u+12v322941v32294ⅆvⅆu

(6)

See Also

indets, Student[Precalculus], Student[Precalculus][ComputationOverview]


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