Question 32006
A parabola is one of the "conic sections", so-called beacause it's one of the curves you get when you slice a right-circular cone in one of several ways.
The other conic sections are:
The circle, the ellipse, and the hyperbola.

You can "see" the parabola when you graph a quadratic equation.
You can tell which way the parabola opens from the sign of the coefficient of the {{{x^2}}}-term.

If this coefficient is positive, the parabola opens upward.
If this coefficient is negative, the parabola opens downward.

In your problem, the quadratic equation is:
{{{y = (-1/2)x^2 + 3}}} and you can see that the coefficient of the {{{x^2}}}-term {{{-1/2}}} is negative, so the parabola opens downward.

Here's the graph of your equation:
{{{graph(300,200,-5,5,-5,5,-(1/2)x^2+3)}}}