The equation y=ax^2 describes a parabola. if the value of a is positive which way does the parabola open

This is very simple as all you would need to do is simply make a table of values and substitute the value of a as +1, and see what coordinates will be obtained, by plugging in any value for X and finding a y coordinate. Now do the process again with -1, and eventually you will see after plotting which direction the parabola will open.