Parabolas ... everywhere you look ...

Talk-to-Me by flickr user photobrick

http://flickr.com/photos/kennethg/13430637/

What we learned from a piece of paper ...

by a similar argument we get ...

What we learned from a piece of paper ...

Let's compare and contrast this with what we've learned before ...

VERTICAL HORIZONTAL

Now you try: Sketch the graph, identify the vertex, focus, equation of the axis of symmetry and the equation of the directrix.

And again: Sketch the graph, identify the vertex, focus, equation of the axis of symmetry and the equation of the directrix.

Sketch the parabola defined by each equation, showing the coordinates of the focus and the equation of the directrix. Also write the equation of the axis of symmetry and the coordinates of the vertex.

Now, let's explore how we move from the standard form to the general form and back again ...

The Circle

Standard Form for the equation of a Circle

Which equations represent circles? Find the radius, and the coordinates of the centre of each circle.