Sal rewrites the equation y=-5x^2-20x+15 in vertex form (by completing the square) in order to identify the vertex of the corresponding parabola. Created by Sal Khan and Monterey Institute …

Sal rewrites a quadratic equation in vertex form and shows how it reveals the vertex of the corresponding parabola. Created by Sal Khan and Monterey Institute for Technology and …

You may know the formula for the vertex's x-coordinate from standard form as x = -b/(2a), or get the vertex from completing the square like Sal did for the first example. However for the …

Sal rewrites the equation y=-5x^2-20x+15 in vertex form (by completing the square) in order to identify the vertex of the corresponding parabola.

What I wanna do in this video is explore a different method that really uses our knowledge of the vertex of a parabola to be able to figure out where the focus and the directrix is going to be.

Want to learn more about finding parabola equation from focus and directrix? Check out this video.

I don't know exactly where it intersects the x-axis but it's going to be a downward opening parabola. Let's do one more example just so that we get really fluent at identifying the vertex …

Now another term that you'll see associated with the parabola, and once again, in the future, we'll learn how to calculate these things and find them precisely, is the vertex.

So given this, how do we figure out the vertex? Well the key idea here is to recognize that your axis of symmetry for your parabola is going to sit right between your two x-intercepts.

This video by Sen Zen explains how to rotate curves, parabolas being one of them; however, it does not talk about how to find the equation given a directrix after a parabola has been rotated: