Creating Quadratic Functions (Equations) from Rational Roots
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Given Rational Roots: ( – 2 ) & ( + 3 ) Locate Roots, Change into Factors, Foil Factors
-4 -3 -2 -1 0 +1 +2 +3 +4
Roots: X = –2 X = +3
Factors: ( X + 2 ) ( X – 3 )
Equation (Function): Y = +X2 –X –6 or F(x) = +X2 –X –6
Changing all signs generates an equivalent but negative quadratic: Y or F(X) = – X2 +X +6
To do this opposite (–) generation change all signs of (X) terms then to check factor equation.
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Given Rational Roots: (– 3 ) & (– 2/3 ) Locate Roots, Change into Factors, Foil Factors
-4 -3 -2 -1 0 +1 +2 +3 +4
Roots: X = – 3 X = +2/3
Factors: ( X + 3 ) ( 3x – 2 )
Equation (Function): Y = +3X2 + 7X – 6 or F(X) = +3X2 + 7X – 6
Changing all signs generates an equivalent but negative polynomial: Y or F(X) = +3X2 + 7X – 6
To do this opposite (–) generation change all signs of (x) terms then to check factor equation.
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Approaching Quadratic Functions, using a nontraditional method ( using roots to generate equations)
allows students to minimize the mystery behind Quadratic Functions and their solution sets (Graphs).
This backdoor approach also provides, a much needed review in multiplication of algebraic expressions:
(Bionomials and Trinomials) which many students need at this stage of their Mathematics development.
Tom Love