The data appears to follow a quadratic curve, and a quadratic model would best describe the data. The quadratic function that models the data is y = 2x^2 - x - 1.
To graph the given data set, we can plot the points on a coordinate plane as follows:
|
8 |
7 | ●
6 |
5 |
4 |
3 |
2 | ●
1 | ●
0 | ●
-1 | ●
-2 | ●
|_____________
-2 -1 0 1 2
From the graph, we can see that the data appears to follow a quadratic curve. Therefore, a quadratic model would best describe the data.
To write a quadratic function that models the data, we can use the standard form of a quadratic equation:
y = ax^2 + bx + c
where a, b, and c are constants to be determined.
To find the values of a, b, and c, we can use the data points and solve the resulting system of equations
-1 = 4a - 2b + c
-2 = a - 2b + c
-1 = c
2 = 4a + 2b + c
7 = 4a + 8b + c
Solving the system of equations, we get:
a = 2
b = -1
c = -1
Therefore, the function that models the data is:
y = 2x^2 - x - 1