ASSIGNMENT 2

by Soo Jin Lee

4.Interpret your graphs. What happens to

(i.e., the case where b=1 and c=2) as a is varied? Is there a common point to all graphs? What is it? What is the significance of the graph where a = 0? Do similarinterpretations for other sets of graphs. How does the shape change? How does the position change?

1. First let's find out the common value to all graphs ,

Since all the graph are having the quadratic formula, the shape if the graphs are parabola.

The common value to all these graphs is distinctively pointed above!

It is '2'!!!!!!

I can see the common value to all the quadratic formula is 'y-intercept'.

2. Now I want to see the significance of the graph , when a=0

Since I want to see the effectiveness of this graph to all the graphs I've drawn above,

I will demonstrate whole graphs!

As I can clearly see through the graph, When a=0, this graph is not a parabola anymore, it is a linear equation so the graph is just the straight line having

tangent 1 and passing (0, 2).

However if a>0 or a<0, the graph will still be the parabola.

In addition, if a>0, the graph is convex and if a<o, the graph is concave.

so a=o is the turning point from convex graph to the concave graph.

3. Do similarinterpretations for other sets of graphs???

How does the shape changes? How does the position changes?

I draw similar graph to the first one, differences are now I shifted the positive x to negative x and I changed the y-intercept to '3'.

Now I have a little difference here,

The common value is '3' since I changed the y-intercept to '3'.

In addition, since y=-x+3 passes through 1,2,4 quadrant, concave and convex parabolas are now divided their positions by that stright line.

When a=0, it changed to the linear equation and this point will be the turning point which will change convex graph to the concave graph!

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