1. Construct graphs for the parabola

Here are the graphs for a=-2,-1,0,1,2
where b and c equal 1.

Notice that when a is positive the function forms a concave-up parabola, and when a is negative the function forms a concave-down parabola. Do you also see that when a=0 we no longer have a polynominal. The function is now linear and therefore forms a straight line. Do these graphs have a common point? We can see that every graph passes through the point (0,1).

Here are the graphs for b=-2,-1,0-1,2

where a and c equal 1.

Notice here that chaning the value of b moves the graph of the function along the x-axis as well as the y-axis. We can see that every graph has a common point of (0,1).

Here are the graphs for c=-2,-1,0,1,2
where a and b are equal to 1.

Here we have changed the values of c in our function. Notice that changing the c value moves the graph of the function along the y-axis, but not the x-axis.

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