Chapter 9.1, Problem 6LC

To determine

The similarities and differences between the graphs of given equations.

Explanation of Solution

Given:

The given equations are:

  $\begin{array}{l}y=-\frac{1}{2}{x}^2\\ y=-\frac{1}{2}{x}^2+1\end{array}$

Calculation:

The input output table can be drawn as:

  

The graphs of the equations will be:

  

Similarities:

• The axis of symmetry for both the graph is x = 0.
• The shape of both the graphs is same.
• Both the parabolas open downwards.

Difference:

• The vertex of one graph is (0, 0) and the vertex of other graph is (0, 1).
• The graphs have same shape but one is shifted from other by 1 unit.