====== Quadratic ======

Quadratic = 2nd Degree [[Polynomial]].

{{ quadratic_1.png|Quadratic 1}}

$$y = x^2$$
$$y = ax^2 + bx + c$$
$$y = ax^2 + 2ax + a^2$$

To visualize:
  * Solve for x to find the roots (where y = 0).
  * The constant is the y-intercept.

==== Complete the Square ====
Make the left-size into some expression squared, taking advantage of the fact that:
$$(a+x)^2 = ax^2 + 2ax + a^2$$

Like this:
\begin{align*}
x^2 + 16x - 57 &= 0\\
x^2 + 16x + 64 &= 57+64\\
(x+8)^2 &= 121\\
\end{align*}

==== Quadratic Formula ====

\begin{align*}
ax^2 + bx + c &= 0\\
x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\end{align*}