Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

To graph $y=(x-4{)}^2$, you shift the graph of $y=x^2$ to the ______ a distance of ______ units.

Step-by-Step Solution

Answer

Shift the graph of $y=x^2$ to the right a distance of 4 units.

Step 1. Given information.

The given equations are:

$$\begin{gathered} y={\left(x-4\right)}^2 \\ y=x^2 \end{gathered}$$

Step 2. Determine the type of shift.

If the argument $x$ of a function $f$ is replaced by $x-h, h>0$, the graph of the new function $y=f(x-h)$ is the graph of $f$ shifted horizontally right $h$ units.

The function $y={\left(x-4\right)}^2$ is in the form of $y=f\left(x-h\right)$, where $h=4$. It means the graph of $y=x^2$ shifts 4 units to the right.

Step 3. Conclusion.

Shift the graph of $y=x^2$ to the right a distance of 4 units.