Parabola: Graph from equation: Simple: Determine the graph of the parabola given by .

We can use the general equation of the parabola: , where the vertex is at (h,k).

First we need to have x² with coefficient 1 in the original problem. Multiplying both sides by 16 will accomplish this: . We can write this so as to reflect the general equation:

From this form and the general equation, we can conclude that h = 0 and k = 0. This means that the vertex is at (0, 0).

Next we determine p, the directed distance from the directrix to the vertex: , or .

This means that the vertex is 4 units above the directrix and the focus is 4 units above the vertex. Since the vertex is at (0, 0), we can conclude that the line y = -4 is the directrix.

Draw your graph from this information, and then check it.