The use for solving quadradic equations for high school students I have a little brother who is in high school and he just learnt the quadratic formula for finding roots of second degree polynomials.
He asked me what why we learn this and how this could apply to a situation in the real world (preferably an application that would apply to his mindset).
I mentioned that the headlight of his bicycle is a parabola, but I was unable to explain why solving a second order polynomial equation like $x^2+3x-2=0$ would apply to this situation.
Could someone help me with some examples?
Thank you in advance

Let $T$ be a triangle and denote the length of its hypotenuse by $x$, and the length of its other two sides by $x-a$ and $x-b$. Then what are the lengths of its sides as a function of $a$ and $b$?
