System Dynamics

Quadratic Forms

The solution to equations of the form \(a x^2 + b x + c = 0\) is \[x = \frac{-b \pm \sqrt{b^2 - 4 a c}}{2 a}.\]

Completing the Square

This is accomplished by re-writing the quadratic formula in the form of the left-hand-side (LHS) of this equality, which describes factorization \[x^2 +2 x h + h^2 = (x + h)^2.\]

Online Resources for Section A.1

Lab setup

Setup diagram for Lab 6.{#fig:lab6-setup .figure color=color}