First order of business today was Algebra, and I learned about parabolas. The graph of an equation of the form y = ax^2 + bx + c is a parabola. However, a parabola can also be defined as the set of all points in a plane that are the same distance a given called the focus, and a given line called the directrix.

Parabolas also have a standard equation. Consider the vertex (h, k), and the axis of symmetry is x = h, and the formula is y = a(x – h)^2 + k.

If a > 0, k is the minimum value of the function and the parabola opens upwards. If a < 0, then k is the maximum value of the equation and opens downwards.

Next up, Marine Biology. I learned about the Chesapeake Bay System, which is made up of five major estuaries, and a bunch of smaller smaller ones. Because it’s so large, there is often a lot of conflict among people on how to use the land and how much of it we should use, for conservation efforts or construction projects.

Animals also the the system in a different way, as a home during different parts of their lives. Oysters live there for their whole lives, while horseshoe crabs are only born there. Sea turtles spend their time there as juveniles, and blue crabs stay there from the larvae stage through adulthood, but aren’t born there.

Lastly, English. Continued with Buddhism, here’s what I learned. Because of the many Buddhas in Mahayana Buddhism, it had to be reconciled with the truth of emptiness, so further explanations were provided, in the three bodies of the Buddha. The bodies represent different understanding, and go as such.

The first body is Dharmakaya, emptiness itself, and the essential body of Buddha.

The second is Sambaghakaya, the body of enjoyment, and the body of Buddhas in the pure lands.

Lastly is Nirmanakaya, the physical body of Siddhartha Gautama, or the physical body of a Buddha. It is an image manifested in the world for the benefit of lower beings.