MATA30H3 Lecture Notes - Long Division, Coefficient, Algebraic Equation
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MATA30H3 Full Course Notes
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Document Summary
Polynomial expression has the form: anxn+an-1xn-1+an-2xn-1+ + a3x3+ a2x2+ a1x+ a0. Degree: the highest exponent on variable x, which is n. Power functions: y = a*xn , n ei. Even degree power functions may have line symmetry along y-axis. Odd degree power functions may have point symmetry about origin. Polynomial functions have 0 to maximum of n x-intercepts, where nis the degree. Polynomial functions can also have at most n 1 local max/mins, where n is the degree. X intercepts are the roots of the function. Factors of a factored form equation are also the roots. Roots can have different orders, and are graphed differently: Passes through intercept like y = x3 at the origin. Transformations of polynomial functions of the form y = a [ k (x-d) ]n + c : a >= 1 : vertical stretch by a factor of a. 0 <= a <= 1 : vertical compression by factor of a.
