Q. 61 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The graph is   and the graph is 

Step 1: Given information

Given the equation $$\begin{gathered} y=x^2 \\ y={(x-2)}^2 \\ y={(x+2)}^2 \end{gathered}$$

Step 2: Sketching the graph

The graph is 

Step 3: Checking the graph

Here all graphs are similar to graph $y=x^2$, shifting by $k$ units left or right.

Hence, the graph $y=(x-5{)}^2$ can be obtained by shifting the graph $y=x^2$ by $5$ units to right and graph $y={(x+4)}^2$ can be obtained by shifting the graph $y=x^2$ by $4$ units to left.

Step 4: Sketching the graph

The graph is