Question

How do you tell if a function is quadratic or linear $?$

Answer 1

Describing function as linear or quadratic:

Linear functions are usually represented by a general equation as $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathit{m}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathit{b}$ where $m$ is the slope and $b$ is the $y$-intercept. The graph of linear function will always be a straight line.

Whereas, the quadratic functions are represented as $\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\mathit{a}{\mathbf{(}\mathbf{x}\mathbf{}\mathbf{–}\mathbf{}\mathbf{h}\mathbf{)}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathit{k}$, $a\ne 0$. The graph of quadratic functions is a curve.

Hence, we can tell if a function is linear or quadratic by its equation and graph.