'vertex' form of a quadratic function

[rexboggs5]

I will shortly be teaching students about the 'vertex' form of a quadratic function, ie y = A(x-B)^2 + C, and in particular about the effects on the graph when you change the parameters A, B and C.

I traditionally do this using Graphmatica, WinPlot and/or a graphics calculator, but I think that maybe itcan be done even more effectively using/including ActivStudio.

Does anyone have or know of a flipchart for teaching this particular topic?

Cheers

Rex

[rexboggs5]

I had a play around tonight and came up with the attached flipchart (more a template than an actual flipchart).

The first page has the graphs of 10 quadratic functions (read the notes). On the second page you can use these pre-defined graphs to quickly graph, for example, y = -2(x + 1)^2 - 4

On the 3rd page is a graph. The students have to use their knowledge of the vertex form to give its equation.

Comments, suggestions, improvements?

Cheers

Rex

[davidlloyd]

Hi Rex
While I don't fully understand the maths (I'd like to know what 'vertical stretch' is!), I've added some actions to page 3 to reveal answers. On 'The vertex is' I've used an 'append text' action. On the others I've used the 'Show' action which only works on invisible objects. I though they would work well when explaining the solution with students.

[davidlloyd]

Forgot to post the revised flipchart:o

[rexboggs5]

Thanks, David. Nice addition. [clap]

BTW, a vertical stretch:
Draw a square on a page.
Select it.
Click on the little box in the top middle and drag upwards so the square is now a rectangle that is twice as tall as it is wide. That original shape now has a "vertical stretch" of 2.

The basic graph on the first page of the flp is the red one, which has the equation y = x^2.
All of the other graphs are that graph 'stretched vertically'. For example the green graph has a vertical stretch of 3, which makes the graph steeper. The blue graph has a vertical 'stretch' of 1/2, which in fact means that it is less steep. So it really is a vertical 'compression'.

Hope that helps, at least a bit.

Cheers

Rex

[davidlloyd]

Thanks Rex. I think I've got it!