Applications of Quadratic Equations - Concept
In Algebra I and Algebra II, we sometimes need to solve word problems using quadratic equations. When solving word problems, some common quadratic equation applications include projectial motion problems and Geometry area problems. The most important thing when solving these types of problems is to make sure that they are set up correctly so we can use the quadratic equation to easily solve them.
Alright guys. I'm a Math teacher so I assign all the kinds of homework problems that you're seeing in front of you. But one of the things that I know that my students do, is they skip the word problems and that just gets me right here because I know you guys could do the word problems if you tried. So when you're looking at word problems that have to do with quadratics, meaning your highest exponent on x is squared. You have an x squared term. There's a couple things you might want to look out for.
One really common application of quadratics is things flying through the air. We call it projectile motion. Sometimes it's like a baseball or a soccer ball. Often you'll see a firework problem, sometimes you'll see a diver, something being shot out of a canon. Anything that flies through the air is going to use a quadratic motion because it's like a parabola. And one other thing to think about is that if it's flying through the air like this, it's probably an upside down parabola. Meaning your leading coefficient on x squared is going to be negative. Look out for that.
Another really common application of quadratics is Geometry. It's kind of not fair of us Math teachers because you are probably in an Algebra class and here we go assigning Geometry problems, it's like not fair. But you guys know a lot about Geometry already. Most of the Geometry problems you'll see when it comes top applications of quadratics will involve either area of triangles or perimeters of rectangles, areas of rectangles. That shows up really, really often as well. Things like, a gardener wants to make a rectangular garden where one side length is six feet longer than the other and he wants to have an area of 90 feet or something. That's the kind of problem you're going to run into and you're going to want to think about assigning variables to one side of the garden as well as the other side. Like if this one is x that guy would be x+2 or whatever.
So when you come to these problems, I promise you guys can do them. Don't give up, don't leave anything blank because as a teacher I know that if a student at least tries, and then he or she comes in for help, it helps me help them because I can see what kinds of errors they're making and maybe where they're getting confused.