**Stephani Eckelkamp**

** **

**A More In Depth
Look at the Parabola**

**ax ^{2}
+ bx + c = y**

** **

** **

** **

** **

** **

** **

** **

** **

**All of these equations pass through the point y = 1. We can conclude that the constant c
will effect where the parabola crosses the y axis.**

** **

** **

** **

** **

**In the assignment ÒParabola: Friend of FoeÓ we can see graphs
when b and c are constant. b = 1
and c = 0. Below is an example of
some graphs with a changing.**

** **

** **

** Link to ÒParabola: Friend or FoeÓ
**

** **

** **

** **

** **

** **

** **

The
equation of the parabolas to the left are in the form of x^{2} + x + c
= y, where
c is a constant. The values for c
in the graph are -3, -2, -1, 0, 1, and
2, and 3. From the graph and the equation we can conclude that the
constant c changes where the parabola crosses the y axis.

Now
that we know how the constants effect the parabola, let us look at the first
graph again.

** **

** **

** **

** **

** **

By
looking at the graph above we can see that x^{2} +2x + 1 = y and x^{2}
– 2x + 1 = y. Both of these
graphs cross the x axis at -1 and 1.
We can also see the all of the above graphs cross the y axis at 1. By using this information we can find
the roots of an inverted parabola that crosses through all the vertices of the
above equations.

The black, inverted parabolaÕs equation is:

x^{2} –
1 = y

As we can see, this inverted
parabola has roots at -1 and 1, and has a vertex on the y axis at 1.