Math 2 example statements

by Joe Zeng Jul 7 2016 updated Jul 7 2016

If you can read these formulas, you're in Math 2!

If you're at a Math 2 level, you'll probably be familiar with most or all of these sentences and formulas, or you would be able to understand what they meant on a surface level if you were to look them up.

The [-quadratic_formula] states that the roots of every quadratic expression $~$ax^2 + bx + c$~$ are equal to $~$\displaystyle \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$~$. The expression under the Square root, $~$b^2 - 4ac$~$, is called the [-discriminant], and determines how many roots there are in the equation.

The imaginary number $~$i$~$ is defined as the primary root of the quadratic equation $~$x^2 + 1 = 0$~$.

To solve the system of linear equations $~$\begin{matrix}ax + by = c \\ dx + ey = f\end{matrix}$~$ for $~$x$~$ and $~$y$~$, the value of $~$x$~$ can be computed as $~$\displaystyle \frac{bf - ce}{bd - ae}$~$.

The [-power_rule] in calculus states that $~$\frac{d}{dx} x^n = nx^{n-1}$~$.

All the solutions to the equation $~$m^n = n^m$~$ where $~$m < n$~$ are of the form $~$m = (1 + \frac 1x)^x$~$ and $~$n = (1 + \frac 1x)^{x+1}$~$, where $~$x$~$ is any positive real number.