Quadratic function calculator

A quadratic function is $f(x)=ax^2+bx+c$ (where $a\neq0$). The key to everything is the discriminant:

$\Delta=b^2-4ac \qquad x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}$

When $\Delta>0$ there are two roots, $\Delta=0$ — one (double), $\Delta<0$ — none among the real numbers. The vertex of the parabola is $W=\left(-\dfrac{b}{2a},\,-\dfrac{\Delta}{4a}\right)$.

The calculator also gives the vertex form $a(x-p)^2+q$, the factored form $a(x-x_1)(x-x_2)$, the axis of symmetry, the y-intercept, and draws the graph of the parabola with the vertex and roots marked.