Parabola: Graph from equation: 1st 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 4 will accomplish this: .

Next we must complete the square by adding and subtracting 9:

Finally, we subtract 8 from both sides and factor:

From this form and the general equation, we can conclude that h = 3 and k = 2. This means that the vertex is at (3, 2).

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

This means that the vertex is 1 unit above the directrix and the focus is 1 unit above the vertex. Since the vertex is at (3, 2), we can conclude that the line y = 2 is the directrix.

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