Hello, 1. The problem statement, all variables and given/known data I am trying to determine on what intervals the parabola y=ax^2+bx+c increases/decreases, without resorting to differentiation. 2. Relevant equations 3. The attempt at a solution For the function to be increasing on a certain interval f(x1)>f(x2) for any x1 and x2 on that interval such that x1>x2. Hence, ax1^2+bx1+c>ax2^2+bx2+c. That yields, (x1+x2)>-b/a. How do I derive the expected x>-b/2a from that? That result could be obtained for x1=x2, hence Δ=0, but why is that and why ought it to be used in order to obtain the correct answer?