a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

As great as he was, Harry Houdini didn't master his famous death-defying stunts overnight. He started small, with a pack of cards and a straight jacket. While we strongly recommend not putting your students in straight jackets, we suggest starting small when it comes to graphing functions. And what's easier to draw than a line?

Students should know the slope-intercept form of linear functions, y = mx + b, and how to extract enough information from the equation to be able to draw it. Since two points define a line, two points are all we need. The y-intercept is practically given to us. It's b from the equation. So the y-intercept of the line y = 2x – 3 is -3. Then, any other point will do. Just plug in any old x, and a y will pop out. There's our second point. Connect 'em, and we're golden.

Once students can handle lines, they should move on to the next phase: quadratics. They should already know how to find the x-intercepts of a parabola via factoring, completing the square, or the handy dandy quadratic formula. Then, plugging in 0 for x should give them the y-intercept, and that information should be enough to get a rough idea of the shape of the parabola.

Parabolas have either a maximum or a minimum, but that's it. When the equation is in the standard form y = ax² + bx + c, the a term can tell them whether they're dealing with a maximum or a minimum. It also helps to know that the x-coordinate of the vertex is given by . That gives the students more than enough points to start graphing parabolas. The best aspect to drill into their heads is that these graphs are just visual representations of the function. The x is the input and the y is the output. That won't change.