Lesson Plan

Sketch a polynomial from its factored form, and match it to a graph or a table, using four facts: degree, leading-coefficient sign, zeros with multiplicities, and the y-intercept

Determine both ends' behavior from degree parity and leading-coefficient sign, and explain why the leading term decides the ends

Find all real zeros of a polynomial in factored form, state each zero's multiplicity, and predict crossing or touching with a sign test

State the maximum number of real zeros and turning points a degree-n polynomial can have

Locate a zero in a table of values by a sign change between rows

"Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or quadratic or exponential function that involves a transformation, not in context." "Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or other nonlinear function in a context, or a quadratic or exponential function that involves a transformation in a context." "Understand and use the fact that for the graph of y = f ( x ), the solutions to f ( x ) = 0 correspond to x-intercepts of the graph and f (0) corresponds to the y-intercept of the graph; make connections between the input/output pairs and points on a graph; interpret this information in a context."