Assignment 2 Problem 8 for Kanita
I will investigate several graphs of
the parabola of the form
on the same axes using different values
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
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
< 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.