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I am trying to get a grasp or concept understanding what how trinomials answer questions other than answering questions in an algebra class. I. Looking for the practical application. What does the first term generally represent? I believe it's called the quadratic, but I'm unsure what that means beyond that it's the definition. I know the third term is my constant, which I assume leaves the second as my variable. Sorry if my question seems I ignorant. But I'm really wanting to understand what I'm doing, beyond following formulas and delivering an answer.

bubba
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Quintinium
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    A trinomial is something of the form $a+b+c$. A quadratic is something of the form $ax^2+bx+c$, which is a trinomial. What do you want to ask? –  Mar 08 '14 at 01:47
  • When you say "trinomial", do you mean something like $5x^2 + 3x -7$. Three terms, an "$x^2$" term, an "$x$" term, and a number?? If so, these things are usually called "quadratics". – bubba Mar 08 '14 at 01:48
  • @Quintinium -- I edited grammar and spelling. Please make sure I didn't change your meaning. – bubba Mar 08 '14 at 01:58
  • @SanathDevalapurkar: In America at least, the word "trinomial" in math education refers almost exclusively to quadratic polynomials of a single variable. – Eric Stucky Mar 08 '14 at 01:58
  • @EricStucky Oh. Thanks for the clarification. –  Mar 08 '14 at 01:59
  • @Eric -- Thanks. I'm American (in a way), and I didn't know that. – bubba Mar 08 '14 at 02:09
  • Please do not post effectively the same question you've asked earlier. You showed no interaction with the user who answered your question (linked above). If you have questions regarding an answer already given, please ask, in a comment below the given answer. If you feel you need to expand on the original question, edit the original question. – amWhy Mar 08 '14 at 14:46

2 Answers2

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A practical application of quadratics appears in physics.

Let us consider a coordinate system such that the initial positions of a particle in projectile motion travelling is $(x_0,y_0)=(0,0)$. The equations of motion are $$x(t)=v_xt\\ y(t)=v_{y_0}t-\frac{1}{2}gt^2(g\mbox{ is approximately }9.8m/s^2)$$ Now, one has $t=x/v_x$. Substituting this into $y(t)$ gives $$y(t)=\frac{v_{y_0}}{v_x}x+\left(-\frac{g}{2v_x^2}\right)x^2$$ Now, this is the equation of a quadratic, or, if you prefer, a parabola. This shows that the path of a particle in projectile motion is a parabola.

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There are some examples of "real world" problems here and here that can be solved by using quadratic equations (also known as "trinomials", I have just learned).

Typically, the individual terms don't mean anything special; it's the sum of the three terms that has some meaning, like some distance traveled or some length or area.

bubba
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