Lesson Plan

Identify the degree and the leading coefficient of a polynomial written in standard form, in non-descending order, or in factored form

Predict what a polynomial's graph does at the far left and far right from two facts alone: the parity of the degree and the sign of the leading coefficient

Explain, with a numerical comparison, why the lower-degree terms stop mattering for large $|x|$ — and why "large" can mean very large

Eliminate candidate equations for a given graph using end behavior, without substituting any points

State the maximum number of turning points of a degree-$n$ polynomial as $n - 1$, and explain why it is a maximum rather than a count

Infer a lower bound on a polynomial's degree from the number of turning points visible on its graph

"AF 705. Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c" (score range 33-36, lines 371-372) "F 509. Find the range of polynomial functions" (score range 24-27, lines 286-287) "F 501. Evaluate polynomial functions, expressed in function notation, at integer values" (score range 24-27, lines 260-262) "A 505. Add, subtract, and multiply polynomials" (score range 24-27, lines 238-239)