Assignment 3

Investigation 1

 

Consider the equation ax2+bx+c and to overlay several graphs of y=ax2+bx+c for different values of a, b, or c as the other two are held constant.

 

 

Answer:
We shall hold 2 of the variables constant and allow a, b, or c to equal -3, -2, -1, 0, 1, 2, or 3.

First, lets explore a and leave b and c constant:

 

Equations:

      y = -3x2 + bx + c

      y = -2x2 + bx + c

      y = -1x2 + bx + c

      y = 0x2 + bx + c

      y = 1x2 + bx + c

      y = 2x2 + bx + c

      y = 3x2 + bx + c

 

Graph:

Clearly, the negative variables for a open downward while the positive variables for a open upward, all of the graphs pass through the point (0,1), and they all have different vertices

 

Next, lets explore b and leave a and c constant:

Equations:

      y = x2 - 3x + c

      y = x2 - 2x + c

      y = x2 - 1x + c

      y = x2 - 0x + c

      y = x2 + x + c

      y = x2 + 2x + c

      y = x2 + 3x + c

Graph:

As before, all of the graphs pass through the point (0,1) on the y-axis, open upward, and have different vertices.

 

Finally, lets explore c and leave a and b constant:

Equations:

      y = x2 + bx - 3

      y = x2 + bx - 2

      y = x2 + bx - 1

      y = x2 + bx + 0

      y = x2 + bx + 1

      y = x2 + bx + 2

      y = x2 + bx + 3

 

Graph:

Once again all of the graphs open upwards and have different vertices. None of the graphs share the same coordinate points, and as c increases the vertices of the graphs shift up as well.

 

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