Main Ideas of Adv Pre Calc Ch 2

Main Ideas of Adv Pre. Calc Ch. 2 Class 1 • • Polynomial Quadratic • • Vertex Axis of Symmetry

Main Ideas of Adv Pre. Calc Ch. 2 Class 1 • • Polynomial Quadratic • Vertex (minimum, maximum) • • Axis of Symmetry • • x = -b/2 a Roots, Zero Crossings • • V: (-b/2 a, f(-b/2 a) Solve f(x) = 0 Factor Quadratic Formula Standard Form: y = a(x-h)2 + k

Main Ideas of Adv Pre. Calc Ch. 2 Class 3 • Polynomial • • Leading Coefficient • Determine end behavior Zeros (roots, solutions to f(x ) = 0, (x-a) a factor, (x, 0) x-intercept) • n zeros if n degree • Find zeros algebraically • Find graphically Zeros of Multiplicity k • If k is odd, crosses x–axis • If k is even, touches x-axis without crossing Polynomial with given zeros

Main Ideas of Adv Pre. Calc Ch. 2 Class 4 • Sketching Graphs of Polynomials • • Apply Leading Coefficient Test • Find real zeros • Plot additional points • Draw Graph through points Intermediate Value Theorem

Main Ideas of Adv Pre. Calc Ch. 2 Class 5 • • Long Division of Polynomials Division Algorithm • f(x) = d(x)q(x) + r(x), r(x) = 0 or degree r(x) less than degree of d(x) Synthetic Division Remainder and Factor Theorems • If f(x) divided by (x-k), then the remainder is r = f(k) • (x – k) is a factor if and only if f(k) = 0

Main Ideas of Adv Pre. Calc Ch. 2 Class 6 • • • Rational Zero Test Descartes’s Rule of Signs Upper and Lower Bound Rules

Main Ideas of Adv Pre. Calc Ch. 2 Class 7 • Rational Zero Test • • Descartes’s Rule of Signs • • • Then use Synthetic Division to Test the Zeros Upper and Lower Bound Rules • • How many possible positive zeros How many possible negative zeros Graph the Function to Locate One or More Possible Zeros • • Find all possible zeros While searching in step 3, be alert for an upper or lower bound to help reduce the number of possible zeros When you finally Reduce to a Quadratic, either Factor it or use the Quadratic Formula

Main Ideas of Adv Pre. Calc Ch. 2 Class 8 • • • Complex Numbers Standard form: a + bi Add Subtract Multiply Conjugates Divide Complex Solutions of Quadratic Equation Fundamental Theorem of Algebra Linear Factorization Theorem

Main Ideas of Adv Pre. Calc Ch. 2 Class 9 • • Rational Functions Vertical Asymptotes Horizontal Asymptote Slant Asymptote Holes Domain Graphing Rational Functions