Quadratic formula

For finding the roots of polynomials with degree 2. Still holds for complex coefficients.

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

Completing the square

We can express:

$$a{x}^2+bx+c=a(x-x_0{)}^2+y_0$$

for some global maximum or minimum (a vertex). To find this point, we can apply the first derivative test and set it to 0 (which gives us the $x_0$ value), then substitute that in to find the $y_0$ value.