Chapter 1, Problem 3CR

To determine

To graph : The graph of the given and parent function is to be drawn and its transformation is to be described.

Explanation of Solution

Given information : The given equation is $h(x)=\frac{1}{2}{x}^2$

Graph : The graph of the given function is in the form of quadratic equation as shown below

  

Table for above graph:

X(input)	-1	-2	0	1	2
Y(output)	0.5	2	0	0.5	2

The parent function for the above given equation is $f(x)=x^2$

Graph for the parent function as shown below:

  

Transformation of given function with respect to parent function as shown below:

  

Interpretation :

Both the graphs are parabolas where the graph of the given function $h(x)=\frac{1}{2}{x}^2$ is much wider than the parent function $f(x)=x^2$

Thus, the graph of $h(x)=\frac{1}{2}{x}^2$ is the result of transformation of quadratic parent function $f(x)=x^2$