Assignment
3

Investigation
2

Graphs
in the xc plane.

Consider the equation

Consider the case when c = - 1 rather than + 1.

Below is the graph of several values of c.

These are the equations of those graphed above. The smaller the value of c, the less
curved the graph. Once c=0 the
graph becomes a straight line.

**C=1,
2, 3, 4, 15**

**To see a dynamic graph of
different c values, click **here**. **

When c is positive the graph of the equation looks like the graph below which
is the graph of

When we consider graphing
2x+b=0 in the bx plane, we see that it has an interesting relationship with the
solutions in the xy-plane. That is
to say that 2x+b=0 intersects

where the solutions in the xy-plane are located.

For example, if you click **here** and go to the graph, you can note
that 2x+b=0 intersects

at two points. These two points are (0.697, -1.394) and

(4.302, -8.606).

Using the quadratic formula
to solve in the xy-plane we get,

X=

or
x = 4.303 and .697

The solutions for the
quadratic equations can easily be seen on the graph. When graphing

the solution is x=0.

However, when there are no
real solutions, the graph indicates that the solution is not satisfied in the
region shown. Click **here** to
compare the graph of an equation with no real solutions and one with two real
solutions.