To write the quadratic function in standard form based on the given table, we need to find the quadratic equation that fits the provided values.
Using the points (1, 2), (2, 1), and (3, 2), we can set up a system of equations to solve for the coefficients of the quadratic function.
The standard form of a quadratic function is given by: f(x) = ax^2 + bx + c
Using the point (1, 2):
2 = a(1)^2 + b(1) + c --> a + b + c = 2
Using the point (2, 1):
1 = a(2)^2 + b(2) + c --> 4a + 2b + c = 1
Using the point (3, 2):
2 = a(3)^2 + b(3) + c --> 9a + 3b + c = 2
Solving this system of equations will give us the values of a, b, and c. However, based on the given values, it appears that the relationship is not perfectly quadratic. Nevertheless, we can still approximate a quadratic function based on the provided points.
Solving the system of equations, we find:
a = 1/2, b = -3/2, c = 2
Therefore, the quadratic function in standard form that approximates the given values is:
f(x) = (1/2)x^2 - (3/2)x + 2
I hope this helps! :)