c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

After a while, any magician is bound to get tired of dinky little card tricks. That's usually when they hang up their cape and begin a new hobby like knitting or origami or ice fishing. But not Houdini. When he got bored of foolish wand-waving, he decided to spice things up a bit and mastered the art of escaping death. No biggie.

Well, your students will undoubtedly get bored with quadratics but instead of throwing in their parabolic towels, they'll spice mathematics up with polynomials.

Students should know what polynomials are. Polynomials are just one degree higher than a quadratic. Actually, they can be as many degrees higher as they want, as long as the degrees are positive whole numbers. So the equation y = x⁵ + x⁴ – 4x – 4 is a polynomial, but y = x^8⁄₃ + 3x + 7 is not.

As far as end behavior goes, students should know to look at the highest degree of the polynomial and its coefficient, axⁿ. If n is even, the function will extend either up or down on both ends (as x goes to positive or negative infinity). If n is odd, they'll go in opposite directions. If a is positive, the even powered functions will go up and the odd powered functions will start down and go up. If a is negative, the even powered functions will go down, and the odd powered functions will start up and go down.

The highest order also gives us the maximum number of roots (x-intercepts) the function can have. A function whose highest order is 8 could have, at most, 8 x-intercepts, but it could have 7 or 6 or even 0. Just as before, we can find the zeros by factoring the equation into linear factors and then setting each individual factor to equal 0.

For instance, the equation y = x⁵ + x⁴ – 4x – 4 can be factored into , which has three real roots of x =-1, -, and . And the y-intercept is -4 (since y = 0⁵ + 0⁴ – 4(0) – 4 = -4).

With these rules and point-finding methods up their sleeves, students should be able to draw sketches of polynomials faster than they can pick a card, any card.