Chapter 1.7, Problem 27E

To determine

To compare: the graph of the function with the graph of its parent function.

Explanation of Solution

Given information:

The function is $y=x^2-2$ .

Concept used:

The parent function of the given function is $y=x^2$ .

Calculation:

Sketch the graph of the given function and the parent function.

For the parent function $y=x^2$ construct a table as

  $\begin{array}{cccccccc}x& -4& -2& -1& 0& 1& 2& 4\\ y& 16& 4& 1& 0& 1& 4& 16\end{array}$

Plot these points and join them

  

The obtained graph is the graph of parabola which is opened upward, symmetric about x - axis and vertex is at $\left(0,0\right)$ .

Now for the given function $y=x^2-2$ construct a table as

  $\begin{array}{cccccccc}x& -4& -2& -1& 0& 1& 2& 4\\ y& 14& 2& -1& -2& -1& 2& 14\end{array}$

Plot these points and join them

  

The obtained graph is the graph of parabola which is opened upward, symmetric about x - axis and vertex is at $\left(0,-2\right)$ .

On comparing both the graphs, it can be seen that when the parent function is shifted vertically downward by 2 units, that is 2 units in the negative direction then the given graph that is $y=x^2-2$ is obtained.

Conclusion:

The given graph is 2 units shift in the downward direction of the parent function’s graph.