Final answer:
To find the function f(x) = ax^2 + bx + c, we can use the given values of f(1), f(-3), and f(3) to solve for the coefficients a, b, and c.
Step-by-step explanation:
To find the function f(x) = ax^2 + bx + c, we can use the given values of f(1), f(-3), and f(3) to solve for the coefficients a, b, and c.
Substituting x = 1 into the function gives us: 1a + 1b + c = 6. This can be written as a + b + c = 6.
Similarly, substituting x = -3 gives us: 9a - 3b + c = 22, and substituting x = 3 gives us: 9a + 3b + c = 10.
We now have a system of three equations with three variables which can be solved to find the values of a, b, and c.