Final answer:
To find a formula for a cubic function f, we can use the given information f(1) = 8 and f(-3) = f(0) = f(2) = 0. By creating a system of equations using these points, we can solve for the coefficients of the cubic function.
Step-by-step explanation:
To find a formula for a cubic function f, we can start by using the given information. We know that f(1) = 8, f(-3) = f(0) = f(2) = 0. We can use these points to create a system of equations and solve for the coefficients of the cubic function. Let's assume the general form of a cubic function is f(x) = ax^3 + bx^2 + cx + d.
Using the values f(1) = 8, f(-3) = f(0) = f(2) = 0, we have the following equations:
a + b + c + d = 8
-27a + 9b - 3c + d = 0
d = 0
These three equations can be solved simultaneously to find the values of a, b, c.