# Exploring Quadratic Equations

### Assignment 2

### Erin Horst

Produce several (5 to 10) graphs of

on the same axes using different values for **d**. Does
varying **d** change the shape of the graph? the position?

Let's first begin by exploring the function

We can do this by changing values of **d** and see what
happens to the graph. Let us view a movie
where **d** changes between -5 and 5.

After viewing the movie we can begin to answer the question:
does varying **d** change the shape of the graph? the position?
We can conclude from the movie that **d** shifts the graph
of the functions to either the left or right across the x-axis.
Why is this? Let's recall that when making adjustments to the
identity function y = x, by adding or subtracting values to x,
i.e. y = (x - (-**d**)), y = (x- (**d**)), these adjustments
create a shifting of the graph of the function. We know that if
**d **< 0, then the graph of the function will be shifted
to the left and if **d** > 0, then the graph of the function
will be shifted to the right.

Since we know that the **d** causes the graph to shift horizontally
along the x-axis, we can also realize that **d** will not change
the shape of the graph. Let's recall that to make a graph stretch
or compress we would need to be multiply either the variable x
by some **a** (y = **a**x) or f(x) by some **a** (y =
**a**f(x)).

We have concluded through our exploration that when changing
the **d** within the equation

the graph of the function is shifted horizontally along the
x-axis.

Return