Quadratic Equations

Recall that a linear equation in one variable is of the form $ax+b=0$, where $a$ and $b$ are constants and $a\ne 0$.

For example:

$\begin{array}{l}3x+5=0\\ -6x-2=0\end{array}$

A quadratic equation has an $x^2$ ($x$-squared) term. ("Quadratum" is Latin for square.)

The general quadratic equation in standard form looks like

$a{x}^2+bx+c=0$, . . . . where $a\ne 0$.

If we want to find the $x$ or $x$'s that work, we might guess and substitute and hope we get lucky, or we might try one of these four methods:

We can solve graphically by equating the polynomial to $y$ instead of to $0$, we get an equation whose graph is a parabola. The $x$-intercepts of the parabola (if any) correspond to the solutions of the original quadratic equation.