Solving Quadratic Equations (a.k.a. Parabolas)
"Quadratic Equations" and "Parabolas" refer to the same thing -- equations with an x^{2} in them -- and they're annoying because they keep popping up again and again in every math class you take. First they're in Algebra 1 as equations you have to factor to solve. The second time is in Algebra 2 (or intermediate algebra if you're in college), where you learn that x-squared equations graph as parabolas. Finally, in pre-calc (or advanced algebra) they use them to introduce the polynomial concepts of "zeros" and "roots" and "real and non-real solutions" and "maximia and minima" and all kinds of other fancy function stuff. Well, in the videos below, we'll just do the first kind: "solving" x-squared equations for their "roots" without graphing them. Later chapters will focus on graphing parabolas and finding their maxima and minima (hint: it's gonna be the vertex).
[Btw, if you're not a fan of factoring, definitely go back and check out my factoring chapter first because factoring is key. Also btw, this chapter doesn't cover graphing quadratics (parabolas): that's later in the graphing quadratics and conic sections chapters.
Factoring Quadratic EquationsThe best way to solve a quadratic equation (a.k.a. "find the x-intercepts of a parabola") is factoring, except in the rare case where there's no middle term and you can just square root both sides. (If you're not a fan of factoring, you should check out my factoring chapter.) |
---|
Completing the squareWhile not the most useful quadratic method for most of the students I tutor, there are a few who like it. You should also learn completing the square if you're ever going to feel ready to try deriving The Quadratic Formula on your own. You know, for kicks. |
---|
The Quadratic FormulaOn the down side, you'll have to memorize this puppy. On the up side, this formula is going to save your bacon a lot, both when solving equations that can't be factored and when something can be factored but you can't figure it out. My only warning: whatever you do, don't attempt to learn the quadratic formula song. You'll regret it. |
---|
Quadratic Word ProblemsTeachers vary quite a bit on whether they make you do word problems requiring factoring to solve. I demonstrate a few here, about picture frames with constant borders and farmers trying to construct pens, to give you a flavor of how these things usually go. As always, learn the ones your teacher emphasizes in class! |
---|
Quadratic InequalitiesThis video is all about what to do when your quadratic "equation" suddenly has a "<" or ">" instead of an equals sign. Not surprisingly, to solve "quadratic inequalities" we'll use a fun combination of the "quadratic" methods from this chapter (factoring mostly) and solving inequalities stuff from the previous chapter. |
---|