Chapter 1.6, Problem 47E

Solution

To Write: The equations for the translation graph $G$ from the graph $y$ .

The equation for the graph $G$ is $3{(x-4)}^2$ .

Given:

  $y=x^2$ : a vertical stretch by a factor of $3$ , then a shift right $4$ units.

Calculation:

Consider the function $y=x^2$

The graph of $G$ obtained from the graph $y$ by the sequence of given transformations.

The equation for vertical stretch by a factor of $3$ :

  $G=3y$

Now, substitute $y=x^2$ in the above $G$ function:

  $G=3x^2$

The equation for right shift of $4$ units as:

  $G=3{(x-4)}^2$

Thus, the equation for the graph $G$ is $3{(x-4)}^2$ .