Varying **d**
in the Equation
In this investigation,
I would like to see what happens to the graph of the given function
by changing the value of **d**.
First, I will graph
the function with **d** = -2, -1, 0, 1, 2.
All of the graphs have
a vertex with a y-value of -2. Does this come from the - 2 at
the end of each equation? What happens if it is a + 2 instead?
This leads me to believe
that a quadratic equation written in this form will have a vertex
with a y-value of the number added to the end.
click here to see this investigation as a movie.
(I have let **d**=0 and am calling the number added
to the end **k**. I let **k** run from
-5 to 5.)
Back to the question
at hand -- what happens when the value of **d** is changed?
If **d**
=1, we have:
This graph has a vertex
(1,-2).
If **d**
= 2, we have:
This graph has a vertex
(2,-2).
If **d**
= 3, we have:
This graph has a vertex
(3,-2).
If **d**
= -1, we have:
This graph has a vertex
(-1,-2).
If **d**
= -2, we have:
This graph has a vertex
(-2,-2).
I think that it becomes
very obvious that whenever you have a quadratic equation in this
form, the vertex will lie at: (**d**,**k**).

Return