Algebra - Quadratic Equation #2

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Plotting of graph for the equation

y = (x - a)(x - b)

This simulation uses Java.

(1) Change the values of a, b. See how the graph changes.

 y  = (x - 1000 900 800 700 600 500 400 300 200 100 90 80 70 60 50 40 30 20 10 9 8 7 6 5 4 3 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 -200 -300 -400 -500 -600 -700 -800 -900 -1000 ) (x - 1000 900 800 700 600 500 400 300 200 100 90 80 70 60 50 40 30 20 10 9 8 7 6 5 4 3 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 -200 -300 -400 -500 -600 -700 -800 -900 -1000 )

(After clicking on a drop down box, use the keyboard arrow keys to quickly change the values.)

Zoom: 90 80 70 60 50 40 30 20 10 9 8 7 6 5 4 3 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

(2) What do the values of a and b correspond to, in the graph?

(3) Try to find values of a and b that will

• shift the graph so that it touches the x axis at only one point
• shift the entire graph above the x axis
• flip the graph upside down.

(4) Compare this graph with the graph of

y = ax² + bx + c

Both are quadratic equations, containing x² values. Why are the graphs so different?