The scatterplot to the left shows the cost, C, in thousands of dollars, and living space, z, in square feet (ft) for several houses in a certain neighborhood. According to the data, which of the following best approximates the cost for an additional square foot of living space for homes in this neighborhood?

f(x) = -22.45x^2 + 92.38x + 1.86

Because the points on the scatter plot show an increase in concentration from 0 hours through 2 hours and a decrease from 2 hours through 4 hours, the relationship shown is best modeled using a quadratic function.

Let's look closely at the two quadratic function choices to determine the key features of their graphs.

Because the coefficient of its x^2 -term is negative, the graph of f(x) = -22.45x^2 + 92.38 + 1.86 will be concave down and have a maximum value.

Because the coefficient of its x^2 -term is positive, the graph of f(x) = 22.45x^2 + 92.38 + 1.86 will be concave up and have a minimum value.

Because the scatter plot shown has a concave down trend, the function that best describes the relationship shown is:

f(x) = -22.45x^2 + 92.38 + 1.86

Step-by-step explanation: