Department of Math Education

J. Wilson, EMAT 6680

The Parabola

Lesson #2 - by Jan White

**What happens to y=ax² +
x +2 as a is
varied?**

As a changes the graphs can
be seen to shrink or expand. When the absolute value of a
is greater than 0 then the graph shrinks towards the y-axis and when the
absolute value of
a is less than 0 then the
graph expands towards the x-axis. When a
is negative, this causes the graph to open downwards. The dialation
would remain the same.

**What happens to y=x² + x
+c as c is varied?**

As can be seen by the graphs above, when c
is
varied this will raise or lower the graph determining the y intercept.

**What happens to y=x² + bx
+1 as b is varied?**

As b is varied you can see that
these graph are both dialated and transposed up and down. If we look
a little closer there seems to be a correlation among the vertexes of theses
graphs.
The yellow graph, -x² +1, above is the locus of the
previous graphs as b is varied.

**Summary:**

As a is
varied and b and c are fixed the parabolas become dialated. When
c
is varied and a and b are fixed this either raises or lowers the parabolas.
As b is varied this will decribe the locus
of the parabola y = -x² + c. This is something that would be time
consuming in the classroom to do by hand but is very effective when done
by this graphing program.

RETURN