This equation is in the conic form of a parabola. If you've already forgotten, here's what that looks like: 4p(y – k) = (x – h)2 Let's go through and tackle these, one by one. The vertex is at (h, k). Notice that both h and k are subtracted in the general equation, so we take the opposite of what we see in our equation. The vertex is (-1, 2). Before we go any further, we're going to need p; it tells us the distance from the vertex to both the focus and the directix. The equation tells us that 4p = 8. Then it whispered "Burma shave." We're just going to ignore that. So, p = 2. The positive sign tells us that the parabola points either up or right, depending. The value is the distance we travel to get to the focus and directrix from the vertex. So, does it point up or right? We need to know to find everything else about the parabola. Well, our equation follows the general form of (some y stuff) = (some x stuff)2. We recognize that as an old-school parabola that opens up or down. So, up it is. The focus is going to be even farther up, then, up in the chest of the parabola. Two up, to be precise, from the vertex. That's (-1, 2 + 2) = (-1, 4). The x value doesn't change, just y. The directrix will be below the parabola's vertex. Moving 2 down from the vertex puts us at y = 0. The line of symmetry is perpendicular to the directrix, and it passes through the focus and vertex. You can find the slope between those two and plug them into the equation for a line, or notice that they both have -1 as their x term. The line of symmetry is of the form x = (something), where (something) = -1. |