By Nami Youn

**Write-up
#2**

**Exploring
the graph of **

Introduction

In this write-up, I examine the graphs of the graphs of using the different values of a. The focus is how the graph of appears as a changes.

1. Varying the values of "a", when a is positive

The graph of is a parabola with the vertex at the origin(0 , 0).

(purple), (blue),(green),(yellow)

1) Let's notice the y values .

All the y-values is positive. The squaring operation
makes the result. Also, the parabola never touches the x-axis except at
the origin(0, 0).

2) Now, let's look at the shape of the graphs.

The parabola open up and has a minimum, when "a"
is positive.

3) Finally, notice that the

The graph of
is wider than the graph .
Obviously,
is wider than
.

Therefore. we can see that the graph becomes more narow
as the value of a increases, when a>0. Similary, the graph becomes
wider as the value of a decreases, when a>0.

2. Varying the values of "a", when a is negative

Again, the graph of , a<0 is a parabola with the vertex at the origin(0 , 0).

(purple),(blue), (green), (yellow).

1) Let's notice the y values .

All the y-values is negaitive. Also, the parabola never
touches the x-axis except at the origin(0, 0).

2) Now, let's look at the shape of the graphs.

The parabola opens down and has a maximum, when a is
negative.

3) Finally, notice that the

The graph of
is wider than the graph
. Obviously,
is wider than
.

Therefore. we can see that the graph becomes more narow
as the value of a increases, when a<0. Similary, the graph becomes
wider as the value of a decreases, when a<0.

3. Relation between the graph a>0 and a<0

Let's compare of the following graphs.

(purple), (green)

-4 | -1 | 0 | 1 | 4 | |

16 | 2 | 0 | 1 | 16 | |

-16 | -2 | 0 | -16 | -16 |

For the same x-value, y-absolute values of both of graphs are the exactly same. This means that the graph is reflected over the x-axis. The axis of symmetry is x-axis.