Algebra: Quadratic Equations and Inequalities

Quadratic Equations and Inequalities

When I taught math at a public high school, I also coached track and field for three years. That may shock you (since I am obviously a math geek), and quite honestly, it should. I have never and will never be known for being nimble or possessing quick, dexterous reflexes. In fact, I actually got kicked out of a gymnastics program when I was in elementary school, because they thought I was going to paralyze myself. I am the exact opposite of a cat€”during a fall, most cats right themselves midair and manage to land on their feet. In gymnastics, no matter what position I fell from, or how high I was from the ground, I always managed to fall right on the top of my head.

Regardless, the school administration saw fit to make me coach of the track team, and immediately assigned me the task of training the hurdlers. (As coach, I only tried to hurdle once, and I think I must have knocked myself out doing it, because when I regained consciousness, my face was planted firmly in the track. Interestingly enough, my feet were still propped up on the hurdle.) Even though I was not the most proficient coach in the world, I did learn one thing€”always start training runners with the hurdles at their lowest possible setting. There's no sense starting a new athlete out with the hurdle at its actual, intimidating race height right away. You start easy, and then slowly build the difficulty along the way.

You already know how to solve linear equations, so now I'm going to move the hurdles up a notch. Instead of solving equations containing polynomials of degree 1 (like those equations you solved way back in Solving Basic Equations), it's time to throw in some polynomials of degree 2. You'll have to use completely different techniques than you did for linear equations, but the good news is that you've got three different methods to choose from to do so. By the end of the section, you'll be leaping like a gazelle over the new, higher hurdle, and I'll be quite proud of you, even though I'm down here, unconscious on the ground.

Excerpted from The Complete Idiot's Guide to Algebra © 2004 by W. Michael Kelley. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.

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