which kind of function best models the set of data points (-3,18),(-2,6),(-1,2),(0,11), and (1,27)?
To find the best function that models the given data points, we can try to see any patterns or relationships between the x-values and y-values. By observing the data points, it seems that as the x-values increase, the corresponding y-values also increase.
One type of function that represents this relationship is a quadratic function, which has the form f(x) = ax^2 + bx + c. Let's try to use this form of function to model the given data points.
Substituting the x-values and y-values into the quadratic function form, we get the following system of equations:
When x = -3, y = 18: 18 = a(-3)^2 + b(-3) + c
When x = -2, y = 6: 6 = a(-2)^2 + b(-2) + c
When x = -1, y = 2: 2 = a(-1)^2 + b(-1) + c
When x = 0, y = 11: 11 = a(0)^2 + b(0) + c
When x = 1, y = 27: 27 = a(1)^2 + b(1) + c
Simplifying these equations, we get the system:
9a - 3b + c = 18
4a - 2b + c = 6
a - b + c = 2
c = 11
a + b + c = 27
Using any method of solving systems of equations, we find that the values for a = 3, b = -2, and c = 11 are consistent with all the equations.
Therefore, the best function that models the given data points is f(x) = 3x^2 - 2x + 11.