    Equation for all parabolas

kill(all);

y(x):=a*x^2+b*x+c=0;

    Equation for the maximum or minimum¦

yp(x):=diff(y(x),x)$ yp(x);

yp(x):=2*a*x+b;

x0:first(solve(yp(x),x));

rhs(x0);

y(-b/(2*a));

f(x):=A*(x-h)^2+k;

expand(f(x))=lhs(y(x));

factor(lhs(%));