Question

Given the table of data, determine the function that would most appropriately model the data.

x 1 2 3 4
f(x) 4 3 4 7
a.] exponential
b.] cubic
c.] square root
d.] quadratic

Answer 1

This is clearly a quadratic equation because when you graph it, you get the parabola shape.

Answer 2

We have that the data have a high point at the start (4). Then, it drops to a lowest point (3) and then it increases again. Hence, an exponential fit is a bad idea; exponential functions are always increasing. The same applies to square root functions, they are always decreasing or increasing and they do not have up and downs.
A quadratic function is the most appropriate function to model the data. While it is true that also cubic functions can act like this, the simplest choice is quadratic functions; they have a lowest dip and then they increase on either side of the dip, just like the data.
The correct answer is d.