Given a quintic polynomial [math]f\left(x\right)=\left(x-a\right)\left(x-b\right)\left(x-c\right)\left(x-d\right)\left(x-e\right)[/math] , define [math]x_a=\frac{\left(b+c+d+e\right)}{4}[/math], and similarly [math]x_b=\frac{\left(a+c+d+e\right)}{4}[/math] and [math]x_{c,}x_{d,}x_e[/math]. We then look at the five corresponding points [math]P_a=\left(x_a,f\left(x_a\right)\right)[/math] , and likewise [math]P_b,P_c,P_d,P_e[/math] (these points can be viewed by pressing the first checkbox).[br][br]By clicking the second checkbox you can see the polynomial interpolation of these five points.