graphs. How does the shape change? How does the position change?

Let's see the graph of

when a=-2, -1.5, ..., 1.5, 2.

We can see that as **a **is varied, the width and vertex
of is varied but

all graph pass through **(0,2)**.

**Case 1) a>0**

We can know that the width of the graph is gradually wider
as** a** is close to zero and the verttices are on the left
hand side of the y-axis

**Case 2) a = 0**

Our equation becomes a line

**Case 3) a<0**

Likewise a>0, we can know that the width of the graph is
gradually wider as **a** is close to zero and the verttices
are on the right hand side of the y-axis

**Our Result**

**1) **As
the value of **a** is close to zero, the width of the grapgh
becomes wider

(i.e. as the absolut value of a is decreasing, the width of the grapgh becomes wider)

**2)**
As the value of a is decreasing, the vertex moves towards left-down
passing through (0,2)

**3)**
All graph of the equation above pass through **(0,2)**

**4)**
If a>0 then the grapgh is concave and if a<0 then the graph
is convex

**First**, let's consider carefully
the trace of the vertex of

Explore the trace

We can infer that a trace of the vertices becomes a line passing through (0,2)

**Second**, let's consider
carefully the trace of the vertex of

Explore the trace

We can infer that a trace of the vertices becomes a parabola passing through (0,2)

**Third**, let's consider carefully
the trace of the vertex of

Explore the trace

We can infer that a trace of the vertices becomes a line parallel to y-axis

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