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Teachers & SchoolsStudy Guide

Greetings, mathronaut. We're heading back to the planet of the polynomials to take a closer look at a particularly fascinating subspecies of polynomial, the quadratics. By the time we're done, you'll know them inside and out: how to solve them, how to graph them, their likes and dislikes…you'll even be able to sniff them out when they're in disguise. There will be no hiding from you.

Before we go, though, we need to introduce you to some new types of numbers: imaginary and complex numbers. It turns out that the quadratics are always hanging out with these guys, and we need to be prepared to deal with them, too.

**Paul's Online Math Notes: Equations Reducible to Quadratic Form**

If you want to work with quadratic-like equations, go ask Paul for help. He knows what's what, where's where, and how to do the voodoo that you need to do.

**Purplemath: Complex Numbers Introduction**

Imaginary numbers can take some getting used to. You have to unlearn a rule that's been drilled into your head (don't bother looking; the hole has already healed) and the exponents cycle in a way real numbers don't. This page provides some more help in wrapping your head around all these new ideas.

**The Biology Project: Roots of Quadratic Equations and the Quadratic Formula**

Do you want someone else to explain the quadratic formula and the discriminant to you? What, did we not do a good enough job for you? Oh fine, here you go. We could never stay mad at you.

**Patrick Just Math Tutorials: Completing the Square**

Follow along as Patrick completes the square in real time. It turns out the square was missing a block-shaped piece this whole time, not this L-shaped piece we've been holding onto.

**WSHS Math Rap: Do the Quad Solve**

There are three main methods for solving the quads—that is, quadratic equations—and this song covers them all. If you need help working on your glutes, you'll need a different rap.

**Quadratic Inequalities (Visual Explanation)**

Let no inequality stand unexamined. Follow this video's advice to learn more about the struggles for quadratic social justice.

**Soccer Ball Parabola Drop**

A terrifying video of a soccer ball repeatedly cloning itself in mid-air, using anti-gravity to suspend its progeny in place. They line up to form a series of parabolas, which we must admit is pretty cool-looking.

**Fun With Quadratic Equations**

Insert numbers, get a parabola. Pull sliders, change the parabola. See the function, learn the function, love the function.

**Quia: Caveman Parabola Game**

A caveman is going to be eaten by dinosaurs unless you can correctly answer questions about parabolas. There has to be a reason that this makes sense, but we can't think of it.

**Quadratic Equation Solver**

This site will solve a quadratic equation given in standard form. It works great for double-checking your answers (after double-checking them by hand, of course), but not-so-great for doing your homework for you. It's also nearly impossible to use on a test. You should know by now how you should and should not use this kind of thing, so don't make us regret giving it to you.