What does each term in the trinomial represent and their relation to each other?

Question

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.

Answer 1

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.

Answer 2

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.