# What is the graph of a quadratic function?

Feb 11, 2015

A quadratic function is one of the form
$f \left(x\right) = a x 2 + b x + c$,
where $a$, $b$, and $c$ are numbers with $a$ not equal to zero.

The graph of a quadratic function is a curve called a parabola. Parabolas will open upward if $a > 0$
or downward if $a < 0$

Example: $y = 2 {x}^{2} - 3 x - 1$
$a = 2 \left(a > 0\right)$ so the graph opens upward.

graph{y = 2x^2 -3x - 1 [-10.38, 9.62, -4.68, 5.32]}