Answer:
D. A quadratic function since the points are symmetric about the line .
Step-by-step explanation:
Please consider the complete question.
A travel agency made the table below to represent the profits it make on a certain vacation 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.
First of all, we will graph all the given points on coordinate plane and then join the points to see the graph.
We can see that point (10,500) is symmetric to point (50,500). Point (20,800) is symmetric to point (40,800).
Upon looking at attached image, we can see that the data forms the shape of a downward opening parabola, which is symmetric to line .
Therefore, a quadratic function best represents the given data because the points are symmetric about the line .
