completing the square
Perfect square method
Completing the square is an algebraic technique for rewriting a quadratic expression as a perfect square plus a constant.
The method transforms expressions like x² + 6x + 5 into (x + 3)² − 4, making them easier to solve or graph.
It's essential for deriving the quadratic formula and converting parabola equations to vertex form.
Involving squared terms
- equationMathematical equality assertion
- techniqueSkilled way of performing
- algebraicRelating to variable mathematics
- manipulationUnderhanded control of others
binomial · coefficient · constant · factor · polynomial · expression · simplify · expand
Point where edges converge
- parabolaSymmetrical open plane curve
- axis of symmetryLine dividing congruent halves
- graphingPlotting data visually
- coordinate systemMethod for locating points
opens up · y-intercept · x-intercept · concave · minimum · maximum · transformation · plotting
Underground nutrient absorbers
- zeroesNumerals representing absence
- discriminantFormula determining root nature
- quadratic formulaEquation solving ax²+bx+c=0
- radical signSymbol denoting root extraction
factorization · solving · no solution · x-intercept · extraction
Point where edges converge
- minimumSmallest possible quantity
- maximumGreatest permitted quantity
- extremaFunction's highest, lowest points
- critical pointDecisive juncture in events
quadratic
Involving squared terms
- equationMathematical equality assertion
- techniqueSkilled way of performing
- algebraicRelating to variable mathematics
manipulation · binomial · coefficient · constant · factor · polynomial · expression · simplify · expand · variable
vertex
Point where edges converge
- parabolaSymmetrical open plane curve
- axis of symmetryLine dividing congruent halves
- graphingPlotting data visually
coordinate system · opens up · y-intercept · x-intercept · concave · minimum · maximum · transformation · plotting
roots
Underground nutrient absorbers
- zeroesNumerals representing absence
- discriminantFormula determining root nature
- quadratic formulaEquation solving ax²+bx+c=0
radical sign · factorization · solving · no solution · x-intercept · extraction
vertex
Point where edges converge
- minimumSmallest possible quantity
- maximumGreatest permitted quantity
- extremaFunction's highest, lowest points
critical point · profit maximization · resource allocation · turning point
circle
Curved closed shape
- ellipseConic section curve
- hyperbolaCurve with two branches
- conic sectionsCurves from plane-cone intersections
focus · directrix · center · radius · standard form · derive · locus
completing the squarefactoring
Breaking into multiplicative parts
factorization · trial and error · guess and check · quadratic formula · brute force
completing the squarefactoring
Breaking into multiplicative parts
expanding · decomposition · distributing · decomposing · simplifying
complete, completing, completed, completes, completion, completeness, incomplete, incompleteness, completely