Pre-AP Algebra 2 Goal(s): Identify polynomial functions by degree and type Determine end behaviors, zeros, and number of turning points of polynomials Determine +/- intervals and create a “quick sketch” using sign charts

Polynomial Functions A polynomial function is a term or sum of terms where all exponents are whole numbers and the leading coefficient is a real number A polynomial given in standard form has terms written in descending order of exponents Given a polynomial in standard form, the degree of the polynomial is the greatest exponent

Common Polynomial Functions Degree Type Example Constant y = 14 1 Linear y = 5x – 7 2 Quadratic y = 2x2+x-9 3 Cubic y = x3-x2+3x-6 4 Quartic y = x4+2x-1

Polynomial Functions If the leading coefficient of a polynomial is positive, then the right end of the graph is increasing If the leading coefficient of a polynomial is negative, then the right end of the graph is decreasing If the degree of the polynomial is even, then the left and right ends of the graph have the same behavior If the degree of the polynomial is odd, then the left and right ends of the graph have opposite behaviors

Polynomial Functions To determine the positive/negative intervals of a graph: Determine the zeros of the graph (set each factor = 0) Check values between the zeros to determine if each portion of the graph is positive or negative (no exact y-value is needed) The end behaviors and the +/- intervals should allow you to “quick sketch” the graph without regard to maximum/minimum values