Chapter 9.1, Problem 47PPE

Solution

(a)

To calculate: The value of $a$ so that the graphs are in same quadrant.

The required value of $a$ is $a\ge 0$ .

Given Information:

The given functions are $y=a{x}^2\text{and}y={\left(ax\right)}^2$ .

Calculation:

Consider the given functions $y=a{x}^2\text{and}y={\left(ax\right)}^2$ .

Both the graphs are in same quadrant for any positive value of $a$ .

Thus, $a\ge 0$ .

Thus, the required value of $a$ is $a\ge 0$ .

(b)

To calculate: The value of $a$ so that the graph of $y=a{x}^2$ is wider then the graph of $y={\left(ax\right)}^2$ .

The value of $a$ is $a\ge 1$ .

Given Information:

The given functions are $y=a{x}^2\text{and}y={\left(ax\right)}^2$ .

Calculation:

Consider the given functions $y=a{x}^2\text{and}y={\left(ax\right)}^2$ .

Here $a$ represent the scaling factor for the functions.

For the graph of $y=a{x}^2$ is wider then the graph of $y={\left(ax\right)}^2$ , the value of $a$ for the function $y=a{x}^2$ must be smaller then $y={\left(ax\right)}^2$ .

Hence, the value of $a$ is $a\ge 1$ .