Parabola: Graph from equation: 3rd quadrant: 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 -8 will accomplish this: .

Next we must complete the square by adding and subtracting 16:

Finally, we subtract 24 from both sides and factor:

From this form and the general equation, we can conclude that h = -4 and k = -3. This means that the vertex is at (-4, -3).

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

This means that the vertex is 2 units below the directrix and the focus is 2 units below the vertex. That is, the parabola opens downward. Since the vertex is at (-4, -3), we can conclude that the line y = -1 is the directrix.

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