Atravel 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

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.

c

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.