Graphing ellipses is relatively straightforward once we understand the standard form equation. Recall that the standard form equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h, k) represents the center of the ellipse, and a and b represent the lengths of the semi-major and semi-minor axes respectively.

To graph an ellipse, we can follow these steps:

1. Identify the values of h, k, a, and b from the given standard form equation.
2. Plot the point (h, k) on the coordinate plane, which represents the center of the ellipse.
3. Plot the vertices at a distance of a units from the center along the x-axis. These are the points (h ± a, k).
4. Plot the co-vertices at a distance of b units from the center along the y-axis. These are the points (h, k ± b).
5. Sketch the ellipse by smoothly connecting the vertices and co-vertices with a smooth curve.

Let's take an example to illustrate the process. Suppose we have the equation (x-2)^2/4 + (y+1)^2/9 = 1. We can identify h = 2, k = -1, a = 2, and b = 3. Therefore, the center of the ellipse is at (2, -1), and the vertices are (4, -1) and (0, -1), while the co-vertices are (2, 2) and (2, -4). We can sketch the ellipse accordingly.

Remember, practice is key to mastering this concept!