Sept. 11 Class

Learning Goals: Understand the transformations of the quadratic function.

Today we looked more closely at the quadratic function: f(x) = x².

This function is the basic parabola with the follow graph, domain and range.

I then introduced how to use a graphing calculator to plot this graph.

Those who are using iPhones, iPods or iPads might want to try downloading Quick Graph.

Those who are using Android phones or tablets might want to try downloading Algeo Graphing Calculator.

These are free apps that can help you graph (sorry, I've never used a Blackberry before, but I'm sure they have free graphing apps as well.)

You then split off into groups to examine different transformations of the parabola.

Refer to page 38.

Group 1 graphed: f(x) = x² + k

Notice that the value of 'k' made the parabola move up (positive k) or down (negative k).
This is called a vertical translation.

Group 2 graphed: f(x) = (x–h)²

Notice that the value of 'h' made the parabola move left (negative h) or right (positive h).

This is called a horizontal translation.

Group 3 graphed: f(x) = ax²

Notice that the value of 'a' made the parabola flip over if it was negative.

This is called a reflection.

Notice also that the value of 'a' made the parabola stretch or compress.

Putting it all together we have the function:

Some of you recognized that this is the vertex form of a quadratic equation, good job!

We will soon be able to graph these parabolas without using a graphing calculator!

Homework:

p. 40 #1 (Further Your Understanding)

p. 37 #1-7