Investigate   quardratic equation

                                                 By Na Young

4. What happens to  as a is varied?

 

            Let’s investigate the following graph.

                              Graph

                              

                       

 

     As a is varied from –4 to –1, the graph was made in 3 and 4 quadrant

and as a is varied from 1 to 4, the graph showed in 1 and 2 quadrant.

Being different from other graph, as a=0, a graph is a line y=x+2.

Quadrants showing the graphs are different from a’s sign.

 

Is there a common point to all graphs?

 All graphs have a common point (0,2).

 

What is the significance of the graph where a=0?

When a=0, this graph is not quadratic formula and hence, not parabola.

It is one line that a slope is 1 and passed by 2 in y-axis.

                                   

                                          Graph

                                     

 

Each graph except a=0 shows a parabola and as a’s sign, a graph’s shape is

Convex or concave. Explicitly, for a>0, a graph’s shape is convex and

for a<0, it is concave.

We can investigate that a graph’s shape changed as values of a.

For example, a graph of a=1 is less convex than a graph of a=4.

                      

                                       Graph

 

                          

   In the case of a<0, for example, a graph of a=-1 is less concave than one of a=-3.

                              Graph

 

                      

 

 

  Generally, a graph of a=c(c>0) is less convex than a graph of a=d (d>c).

On the contrary, when a<0, this situation is similar. A graph of a=-c(c>0) is

 less concave than a graph of a=-d (d>c). That is, as |a| is increased,

a grape’s shape is more convex (a>0) or more concave (a<0). The position of

a graph is that for a>0, it shows in 1and 2 quadrant and for a<0, it shows

in 3 and 4 quadrant.

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