A quadratic function can be written in standard form as follows.

Here, $a,$ $b,$ and $c$ can be any real number, and $a\neq 0.$ When written in standard form, it's possible to use $a,$ $b,$ and $c$ to determine characteristics of a quadratic function. $\begin{aligned} \textbf{direction} &: \text{upward when } a>0, \\ &\phantom{:} \text{downward when } a<0 \\ \mathbf{y} \textbf{-intercept} &: (0,c) \\ \textbf{axis of symmetry} &: x=\text{-}\dfrac{b}{2a} \end{aligned}$