1. Quadratic Models 1 Aims: To know what a quadratic is. To know the different graph shapes. To use technology to plot some graphs. To be able to identify key features of a graph. To link the graphs features with it’s equation.

2. What is a quadratic? A quadratic is an equation where the highest power is x 2. They can come in many different forms. Identify which of the following are quadratics. 2x 2 + 3x - 92x 2 + 3x 3 - 9(x+1)(x+3) (x+1)(x+2)(x+3)(x – 1) 2 - 8(x 2 +1)(x-5)

3. Expanded Form Today we are going to look at the expanded form of quadratics. y = ax 2 + bx + c The shape of a quadratic graph is always a parabola.

7. Parabolas y = ax 2 + bx + c

9. Graphing We are now going to plot some quadratics to investigate their graphs. There are six questions on page 2 of your booklet that I would like you to plot.

10. On the i-pads Load up the geogebra i-pad app. You can type in your equation in the input bar along the bottom. Zoom in or out as appropriate to get a good view. Make a copy of the sketch in your booklets and label important points on the graph.

11. On a laptop Visit http://www.geogebra.org/cms/en/download / http://www.geogebra.org/cms/en/download / Click Java Webstart Hopefully geogebra will load! You can type in your equation in the input bar along the bottom. Zoom in or out as appropriate to get a good view. Print screen your graphs and copy into word. Crop and label appropriately.

12. On a laptop Visit http://my.hrw.com/math06_07/nsmedia/tools /Graph_Calculator/graphCalc.html http://my.hrw.com/math06_07/nsmedia/tools /Graph_Calculator/graphCalc.html Or google online graphic calculator and click the top link. You can type in your equation in the input bar at the top. Zoom in or out as appropriate to get a good view. Print screen your graphs and copy into word. Crop and label appropriately.

13. On a graphic calculator Press MENU Choose GRAPH mode Type your equation in on the first line. Press SKETCH. If you are having problems with the view press V-WIN -> STD to reset the scales. Make a copy of the sketch in your booklets and label important points on the graph.