**Assignment 2 Problem 8 for Kanita
DuCloux**
I will investigate several graphs of
the parabola of the form
on the same axes using different values
for d.
I will observe the effects varying d has on the *shape* and
*position* of the graph.
The general form of the parabola is
,
with parameters a, h, and k. Where
the vertex is (h, k) and the axis of symmetry is x = h. In my
example, I will let h = d.
I'll begin by observing the graph
where a =1, d = 0, and k = -2.
Notice that the vertex is ( d, k) or
(0, -2) and the axis of symmetry is
x = d or x = 0 in this case. The equation
has two real roots ( one positive and one negative) where the
graph intersects the x-axis. Since a = 1 and for a > 0, the
graph opens upward.
Now let's observe several graphs where
d >
0.
Allowing d > 0, causes the graph to
shift to the right d units. The vertex is (d, -2), so changing the value
of d effects
the position of the vertex, it also shifts the the right d units. However,
the basic shape of the graph does not change. These equations
also have two real roots.
Let's investigate what happens when
d
< 0.
When d
< 0, the graph shifts to the left d
units and the vertex (d, -2) also shifts to the left d units. The
axis of symmetry is x = d. Again, the basic shape of the graph
does not change.
To summarize, changing
the value of d in the equation
causes the graph to shift either to
the left for d < 0 or the the right for d > 0 and the vertex
(d, -2) also shifts to the left or right. The graph opens upward
because a =1(a>0) and the baisc shape of the graph is not effected
by changing d. There are two real roots for each equation.

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