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Quadratic Functions to Vertex Form - (3.6) 2 Methods: Complete the square (be careful if x-squared term doesn't have a 1 coefficient), or Use vertex formula to find h and k and fill in the blanks. h=-b/2a, k=f(-b/2a) Graphing Quadratic Functions - (3.6) positive a, opens up. Negative a, opens down. Vertex, h=--b/2a. k= f(-b/2a). Axis of symmetry, x=-b/2a. Domain of sum, difference, or product of 2 functions - (3.7) Domain is the intersection of the domains of the 2 original functions. That is, find the domain of f. Then find the domain of g. Then put them together. Domain of quotient of 2 functions - (3.7) Domain is the intersection of the domains of the 2 original functions. Also exclude any value that makes the denominator function=0. For f/g: Find the domain of f. Find the domain of g. Find any values that make g=0. Put them all together. Composite functions - (3.7) Use one function as the input to the other function. Pay careful attention to which function comes first and which comes second. The second is the input. Domain of Composite Functions - (3.7) Domain is the intersection of the domain of the inside function and the domain of the composite. For f(g(x)): Find the domain of g. Find the domain of the combination, f(g(x)). Put the two together. Graphing polynomials - (4.1) Find the zeros (x-intercepts) by setting equation equal to zero and solve. Consider multiplicity and end behavior or test points to draw graph. Long division - (4.2) Include every power of x in the dividend. Line up like terms after multiplication step.Synthetic division - (4.2) Include every power of x when writing out coefficients. Number in the box is the opposite sign as the resulting factor. Find the zeros of a polynomial - (4.4) List c=factors of constant. d=factors of highest order coefficient. Find ratio c/d. Test values with synthetic division. Rational functions - Finding holes - (4.5) Holes exist where the same factor appears in the numerator and denominator. Rational functions - Vertical Asymptotes - (4.5) Set denominator equal to zero. Result will be a line, not a point (for example, x=2)