Question

How can you tell if parabola is opened upward or downward just by looking at an equation?

Answer 1

If the coefficient of the x^2 term is negative, it opens down.

Answer 2

let a be the signature of x^2 term in an equation defining a parabola f(x)=a*x^2+b*x+c;
if a>0, there will be no values of f(x) smaller than f(0); similar goes for negative a.