In the shadowy dawn of algebraic discourse, where the ancients wielded clay tablets, we begin our exploration of the quadratic form: ax2 + bx + c. Have ye not felt the lure of its vertex, the siren song of its parabolic trajectory?
Suppose, dear learner, you are tasked with situating stability in your domain, a kingdom beset by the whims of
polynomials. Have you calculated the derivative of your realm's prosperity? Should this derivative be negative, take heed.
Investigate the Derivatives you Know
Now, follow the golden rule of quadratics: If the coefficient of your x2 term, that dominant arbiter
of fate, is greater than zero, stability shall dance upon your axis. Ye shall secure thy quadratic to be a
faithful friend if its roots remain imaginary, lest they descend into your kingdom as hostile entities.
Understand Reality and its Imaginary Roots
Reflect now upon an older time, where quills and cauldrons converged upon mystical processes. "Stability," they
would chant, "is not the absence of motion, but the equilibrium of forces greater than oneself."
A passage known to but a few.
The Great Equilibrium