Student[Precalculus]
CompleteSquare
transform quadratic expressions to completed square form
Calling Sequence
Parameters
Description
Examples
CompleteSquare(f, x, ...)
f
-
algebraic expression, equation, or an inequality involving algebraic terms
x
(optional) name, function, list, or set
...
(optional) name or function
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+c−b24a.
For a step-by-step solution that completes the square, see CompleteSquareSteps.
withStudentPrecalculus:
CompleteSquare3x2+2x,x
3x+132−13
CompleteSquarex21−y3+2y2x−y,x
1−y3x+y21−y32−y−y41−y3
CompleteSquare1sint2+2sint+1,sint
1sint+12
CompleteSquarea2+b2+a+b,a,b
b+122+a+122−12
CompleteSquarex2−x=y2+2y+3
x−122−14=y+12+2
CompleteSquareIntIntu2+2uv2−3v,v,u,u,v
∫∫u+12v−322−94−1v−322−94ⅆvⅆu
See Also
indets
Student[Precalculus][ComputationOverview]
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