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

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Aug 8, 2015

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

Explanation:

Any expression that can be written in the form:
$XXXX$ $color(white)("XXXX")$ $f (x) = a x^{2} + b x + c$ $f(x) = ax^2+bx+c$
is a quadratic function.

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

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

Aug 8, 2015

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

$A x^{2} \pm B x \pm C$ $Ax^2 pm Bx pm C$ is quadratic
where $A \neq 0$ $A != 0$ and $B$ $B$ and $C$ $C$ are anything real

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

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