Problems and explorations with second degree equations.

by Brook Buckelew

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.