Parabolas - At A Glance

Last Saturday we were sitting around the house, bored and watching TV. We were flipping channels when we found something interesting on, or at least wasn't trying to sell us something. It was a program called "Conics: The Infinite Frontier." It was this, reruns of last week's soap operas, or going outside. The decision to keep watching wasn't that hard to make.

The episode was all about parabolas. They must have had a big special effects budget, because the show went all out with the sweeping views of the parabolas curves. It was filled with information, too, including some parts of the parabola we had never heard of: the focus and directrix.

We took notes on the show, and now we're going to share them with you. Look, it was a really boring Saturday, okay?

Example 1

What are the vertex, focus, directrix, and line of symmetry for 8(y – 2) = (x + 1)2?


Example 2

Graph the parabola (y + 2)2 = -12(x – 4).


Example 3

Convert y2 – 2x = 3y + 7 into conic form.


Exercise 1

Find the vertex, focus, directrix, and line of symmetry of y = 8(x – 5)2 + 2.


Exercise 2

Find the vertex, focus, directrix, and line of symmetry for (y + 5)2 = -8(x + 4).


Exercise 3

Graph (y – 2)2 = 3(x + 1).


Exercise 4

Convert y2 + 6y + 4x + 1 = 0 to the conic form of a parabola.


Exercise 5

Convert y = x2x – 1 to the conic form of a parabola.