Algebra - Quadratic Equation Computer Simulation

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Plotting of graph for the equation

y = ax² + bx + c

This simulation uses Java.

(1) Change the values of a, b, c. See how the graphs change.

y

=

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 x2

+

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.)

(2) The yellow graph can be visualized as being created by adding the red and blue graphs together.

y1 = .x2

,

y2 = .x + .

y

=

y1

+

y2

(3) The roots of the equation are the values of x when the graph cuts the x axis (that is, when y = 0). If the graph is entirely above the x axis, the roots are imaginary (contains the square root of -1).

Using the roots, the equation can also be written as

y = (.) (.)

(4) Why does the shape of the graph look different at different zoom levels? Shouldn't it stay the same?

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