# Obtaing a desired quadratic equation

1. Jan 22, 2012

### tsumi

1. The problem statement, all variables and given/known data

Get an inverted quadratic equation ($-x^2$) with maximum y=100 and roots x=0 and x=1/120.

2. Relevant equations

3. The attempt at a solution

I tried changing the several terms of the quadratic equation, used the quadratic formula setting c=100, and x=0 with the negative root and x=1/120 with the positive root, among other less smart attempts. Could not get something reasonable.

Does anyone know how to do it? It does not seam that much difficult, maybe my academic formation is just weak.. =\

2. Jan 22, 2012

### ehild

Hi tsumi,

You need to find the function y(x)=ax^2+bx+c, which crosses the x axis at points x1=0 and x2=1/120, and its maximum is 100=y(max). Or you can write out the function in the form y=C-a(x-b)^2. In this case C=100 as you said, and the maximum is at x=b. Where is the position of the peak of a parabola with respect to its zero points?

ehild

Last edited: Jan 22, 2012
3. Jan 23, 2012

### epenguin

What you seem to be missing (I was not able to understand what you did) is that with roots , α, β, ... the equation
(x - α)(x - β) = 0 is satisfied. And so on for as many roots as there are. This is coming at it from the solved side so to speak - you have probably had more emphasis from the unsolved side.

The conditions you are required to satisfy involve more than the roots, in fact you need an equation of form

A(x - α)(x - β) = 0,

where A is a constant. You are being asked then also to find the A that gives you the maximum stated. If you revise (or work it out) you will find that an extremum for a quadratic is localised halfway between any real roots; however do not just blindly apply that without understanding where that comes from, certainly in your book, or work out self, otherwise you will not have benefited and made self able to solve next time.