f(x) =2x2 + 4x + 3 f(x) =2(x + 1) f(x) =2(x + 1)2 + 1

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f(x) =2x2 + 4x + 3 f(x) =2(x + 1)2 - 2 + 3 f(x) =2(x + 1)2 + 1 Completing the square f(x) = a(x + b)2 + c Easy to graph functions & graphs 1 4 5 2 -2 -2 -4 -2 Factor Theorem x = a is a factor of f(x) if f(a) = 0 1 2 1 f(x) =2x2 + 4x + 3 f(x) =2(x + 1)2 - 2 + 3 f(x) =2(x + 1)2 + 1 (x+2) is a factor since no remainder If finding coefficients Sim. Equations Discriminant of a quadratic is b2 -4ac Polynomials Functions of the type f(x) = 3x4 + 2x3 + 2x +x + 5 Degree of a polynomial = highest power b2 -4ac > 0 Real and distinct roots Tangency b2 -4ac < 0 No real roots b2 -4ac = 0 Equal roots