The graph of such an equation opens downwards when the coefficient of the [tex]x^2[/tex] term is negative. For example, when the equation is in the form [tex]y=a(x-h)^2+k[/tex], the graph opens downwards when a is negative. This is because in such an equation, there is a maximum value and many smaller values, whereas in an equation when a is positive, there is a minimum value with many larger possible values.
