# Is f(x)=x^2-1 a quadratic function?

Aug 8, 2015

$f \left(x\right) = {x}^{2} - 1$ is a quadratic function

#### Explanation:

Any expression that can be written in the form:
$\textcolor{w h i t e}{\text{XXXX}}$$f \left(x\right) = a {x}^{2} + b x + c$

$f \left(x\right) = {x}^{2} - 1$
is equivalent to $f \left(x\right) = 1 \cdot {x}^{2} + 0 \cdot x + \left(- 1\right)$

The fact that the coefficient of $x$ is $0$ does not prevent this from being a quadratic function.

Aug 8, 2015

Any function containing the highest degree as $2$ is quadratic. So:

$A {x}^{2} \pm B x \pm C$ is quadratic
where $A \ne 0$ and $B$ and $C$ are anything real

$A {x}^{3} \pm B {x}^{2} \pm C x \pm D$ is not (it's cubic)
where $A \ne 0$ and $B$, $C$, and $D$ are anything real