Question

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

Short answer

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

Step-by-step solution

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 of4 units.