Chapter 9.1, Problem 48PPE

Solution

(a)

To fill the blank to make the statement complete.

The graph of $y=a{x}^2+c$ intersects the x axis in two places when either of the value $a\text{or}c$are negative.

Given Information:

The given statement is “ The graph of $y=a{x}^2+c$ intersects the x axis in two places when _____”

Explanation:

Consider the given function $y=a{x}^2+c$ .

The function will cuts the x axis at two points when either of the value $a\text{or}c$ are negative.

Hence, the graph of $y=a{x}^2+c$ intersects the x axis in two places when either of the value $a\text{or}c$are negative.

(b)

To fill the blank to make the statement complete.

The graph of $y=a{x}^2+c$ does not intersects the x axis when both the value $a\text{or}c$are either positive or negative.

Given Information:

The given statement is “ The graph of $y=a{x}^2+c$ does not intersects the x axis when _____”

Explanation:

Consider the given function $y=a{x}^2+c$ .

The function does not cuts the x axis whenboth the value $a\text{or}c$ are either positive or negative.

Hence, the graph of $y=a{x}^2+c$ does not intersects the x axis whenboth the value $a\text{or}c$are either positive or negative.