Chapter 8, Problem 2CT

To determine

To draw: the Graph for given function and compare the given graph to a parent function.

Explanation of Solution

Given information:

Parent function:

Transformed function:

Graphing the function:

Comparing this equation with the vertex form of quadratic equation:

  

  

On comparing we find that, the vertex ( h, k ) is and .

As the value of a is a negative number, so the graph will open down.

Now, take some random points of x and y to plot more points on graph:

x	y
-2	-2
2	-2

Now plot these points on the graph:

Therefore, the graph is

  

Now, let us make the graph of .

Comparing this equation with the vertex form of quadratic:

  

  

On comparing we find that the vertex of equation ( h, k ) is and .

As the value of a is a positive number, so the graph will open up.

Now take more points to plot on the graph:

x	y
2	4
-2	4

Now plot these points on the graph:

  

Let us compare the graph of and graph of .

We could see .

Also, if we compare y -coordinate value of point (-2,4) by y -coordinate value of point (-2,-2),

  

Therefore, the graph of g( x) is reflected across x -axis and compress vertically by a factor of of function