Vertex form of the Parabola
I'm just testing out an idea I had. I'll use the Whiteboard to embed a quick lesson on the parabola.
Parabolas are the curved graph that you see if you have a quadratic polynomial. There are a couple ways to write a quadratic polynomial, but the easiest for graphing is vertex form.
The vertex of a parabola is the point of symmetry at the bottom of a parabola (or the top for an upside-down parabola). In vertex form, the coordinates of the vertex can be read right from the equation. The y-coordinate, much like the intercept for a straight line, is just the number that's added at the end. The x-coordinate is inside the exponent, and has a minus-sign in front. If the inside of the exponent is (x-2), the graph is shifted to the right. Can you see why?
Play around with it here. Double click on one of the "a= " or "b= " to edit the number and see how the graph responds: