Complete the Square - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.
Our website is currently undergoing maintenance, which may result in occasional errors while browsing. We apologize for any inconvenience this may cause and are working swiftly to restore full functionality. Thank you for your patience.

Online Help

All Products    Maple    MapleSim


Student[Precalculus]

  

CompleteSquare

  

transform quadratic expressions to completed square form

 

Calling Sequence

Parameters

Description

Examples

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+b2a2+cb24a.

• 

For a step-by-step solution that completes the square, see CompleteSquareSteps.

Examples

withStudentPrecalculus:

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)

CompleteSquareIntIntu2+2uv23v,v,u,u,v

u+12v322941v32294ⅆvⅆu

(6)

See Also

indets

Student[Precalculus]

Student[Precalculus][ComputationOverview]

 


Download Help Document