Question

A travel agency made the table below to represent the profits it make on a certain vacation package.

Number of People vs. Profit
Number of People Who Buy the Package, x
Profit per Person (in dollars), f(x)
10 500
20 800
30 900
40 800
50 500

Which of the following explains the best model for the data in the table?

A)an absolute value function since the values increase and then decrease
B)an exponential function since the ratio of the y-values are about the same.
C)a linear function since the function changes at a rate of 30 dollars per person
D)a quadratic function since the points are symmetric about the line x = 30

Answer 1

Answer: D) a quadratic function since the points are symmetric about the line x = 30

Step-by-step explanation:v

When we plot the given points on the graph we see that,

A parabola appears opening downwards about the line x = 30 because the point (10,500) is symmetric to point (50,500) and point (20,800) is symmetric to point (40,800).

Since, Parabola is the shape of graph of quadratic function.

Hence, Option D) a quadratic function since the points are symmetric about the line x = 30 is correct.

Answer 2

Answer: D) a quadratic function since the points are symmetric about the line x = 30

Explanation:

Here, the given table,

Number of people 10 20 30 40 50

Profit per person 500 800 900 800 500

Since, when we plot the given point we found that,

About the line x = 30,

(10,500) is symmetric to (50,500)

And, (20,800) is symmetric to (40,800)

Also, with help of regression, we found that the function for the given point is,

`f(x) = 60 x - x^2`

Which is a quadratic function.

Thus, Option D) a quadratic function since the points are symmetric about the line x = 30 is correct.