Curve Sketching

Mathematics: Multiplicity and Curve Sketching

Roots of multiplicity r A root of a polynomial is a value of \(x\) for which \(P(x)=0\) For example, \(P(x)=x^2+6x+9\) can be expressed as \((x+3)^2\) In this case, \(-3\) is a root of multiplicity 2 of \(P(x)\) Roots of multiplicity 1 are also known as “single roots” Roots of multiplicity 2 are also known as “double roots” Roots of multiplicity 2 are also known as “triple roots” Curve Sketching Graphs with multiple roots have specific rules for sketching Rules for Leading Coefficient and Degrees The table below explains what happens as a graph approaches infinity and negative infinity, based on the leading coefficient and degree: Degree: OddDegree: EvenLeading Coefficient: PositiveUp Arrow: 1st Quadrant
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