Q. 60 - Precalculus Enhanced with Graphing Utilities

Question

Exploration Graph $y=x^2$ Then on the same screen graph $y=x^2+2$, followed by $y=x^2+4$, followed by $y=x^2-2$. What pattern do you observe? Can you predict the graph of $y=x^2-4$? Of $y=x^2+5$ ?

Step-by-Step Solution

Answer

The graph is   and the graph is 

Step 1: Given information

Given the function

 $$\begin{gathered} y=x^2 \\ y=x^2+2 \\ y=x^2+4 \\ y=x^2-2 \end{gathered}$$

Step 2: Sketching the graph

The graph is 

Step 3: Checking the graph

We get that all graphs are similar to graph $y=x^2$

Hence the graph $y=x^2-4$ is obtained by shifting the graph $y=x^2-4$ units downwards.

Similarly, the graph $y=x^2+5$ is obtained by shifting the graph $y=x^2+5$ units upwards.

Step 4: Sketching the graph

The graph is