This is the equation of a sideways parabola with its vertex at (2009,0). The parabola opens to the left and right. The horizontal axis of symmetry is the line x=2009.

To graph this parabola, we can start by plotting the vertex at (2009,0). Then, we can use the equation to find a few more points.

When y=5, we have:

25-25=8(x-2009)^2

0=8(x-2009)^2

This tells us that the parabola intersects the line y=5 at x=2009.

When y=10, we have:

25-100=8(x-2009)^2

-75=8(x-2009)^2

This tells us that the parabola intersects the line y=10 at two points:

x=2009-√(75/8) and x=2009+√(75/8)

We can continue to find more points by plugging in different values of y. Alternatively, we can recognize that the equation is in standard form and use the properties of sideways parabolas to sketch the graph.

The standard form of a sideways parabola is:

(y-k)^2 = 4p(x-h)

where (h,k) is the vertex and p is the distance from the vertex to the focus.

In this case, the vertex is (2009,0) and p=√(25/8).

So, we can sketch the graph by plotting the vertex and the focus (2009+p,0) and (2009-p,0). Then, we can draw the parabola so that it is symmetric with respect to the axis of symmetry x=2009 and passes through the focus.

The graph should look like this:

https://www.desmos.com/calculator/5qjzvzqj7d