Chapter 2.3, Problem 12E

A.

To determine

To find : The possible points on the given parabola.

Answer to Problem 12E

The point $\left(-6,-1\right)$ is not the possible coordinate of the point $P\left(x,y\right)$ .

Explanation of Solution

Given information : Coordinate of the point $\left(-6,-1\right)$ and graph

  

Since, the point $P\left(x,y\right)$ lies in the fourth quadrant. Therefore, the coordinate of the point will be of the form $\left(a,-b\right)$ where $a,b\ge 0$ .

The given point $\left(-6,-1\right)$ is not of the form $\left(a,-b\right)$ .

Thus, it is not the possible coordinate of the point $P\left(x,y\right)$ .

B.

To determine

To find : The possible points on the given parabola.

Answer to Problem 12E

The point $\left(3,-\frac{1}{4}\right)$ is the possible coordinate of the point $P\left(x,y\right)$ .

Explanation of Solution

Given information : Coordinate of the point $\left(3,-\frac{1}{4}\right)$ and graph

  

Since, the point $P\left(x,y\right)$ lies in the fourth quadrant. Therefore, the coordinate of the point will be of the form $\left(a,-b\right)$ where $a,b\ge 0$ .

The given point $\left(3,-\frac{1}{4}\right)$ is of the form $\left(a,-b\right)$ .

Thus, it is the possible coordinate of the point $P\left(x,y\right)$ .

C.

To determine

To find : The possible points on the given parabola.

Answer to Problem 12E

The point $\left(4,-\frac{4}{9}\right)$ is the possible coordinate of the point $P\left(x,y\right)$ .

Explanation of Solution

Given information : Coordinate of the point $\left(4,-\frac{4}{9}\right)$ and graph

  

Since, the point $P\left(x,y\right)$ lies in the fourth quadrant. Therefore, the coordinate of the point will be of the form $\left(a,-b\right)$ where $a,b\ge 0$ .

The given point $\left(4,-\frac{4}{9}\right)$ is of the form $\left(a,-b\right)$ .

Thus, it is the possible coordinate of the point $P\left(x,y\right)$ .

D.

To determine

To find : The possible points on the given parabola.

Answer to Problem 12E

The point $\left(1,\frac{1}{36}\right)$ is not the possible coordinate of the point $P\left(x,y\right)$ .

Explanation of Solution

Given information : Coordinate of the point $\left(1,\frac{1}{36}\right)$ and graph

  

Since, the point $P\left(x,y\right)$ lies in the fourth quadrant. Therefore, the coordinate of the point will be of the form $\left(a,-b\right)$ where $a,b\ge 0$ .

The given point $\left(1,\frac{1}{36}\right)$ is not of the form $\left(a,-b\right)$ .

Thus, it is not the possible coordinate of the point $P\left(x,y\right)$ .

E.

To determine

To find : The possible points on the given parabola.

Answer to Problem 12E

The point $\left(6,-1\right)$ is the possible coordinate of the point $P\left(x,y\right)$ .

Explanation of Solution

Given information : Coordinate of the point $\left(6,-1\right)$ and graph

  

Since, the point $P\left(x,y\right)$ lies in the fourth quadrant. Therefore, the coordinate of the point will be of the form $\left(a,-b\right)$ where $a,b\ge 0$ .

The given point $\left(6,-1\right)$ is of the form $\left(a,-b\right)$ .

Thus, it is the possible coordinate of the point $P\left(x,y\right)$ .

F.

To determine

To find : The possible points on the given parabola.

Answer to Problem 12E

The point $\left(2,-\frac{1}{18}\right)$ is the possible coordinate of the point $P\left(x,y\right)$ .

Explanation of Solution

Given information : Coordinate of the point $\left(2,-\frac{1}{18}\right)$ and graph

  

Since, the point $P\left(x,y\right)$ lies in the fourth quadrant. Therefore, the coordinate of the point will be of the form $\left(a,-b\right)$ where $a,b\ge 0$ .

The given point $\left(2,-\frac{1}{18}\right)$ is of the form $\left(a,-b\right)$ .

Thus, it is the possible coordinate of the point $P\left(x,y\right)$ .