Final answer:
To find a cubic function using algebra, we can use the given three points to solve for the coefficients a, b, c, and d. By substituting the values and solving the system of equations, the cubic function is y = -0.5x^3 - 3x^2 - 2.5x - 3.
Step-by-step explanation:
To find a cubic function using algebra, we can use the form y = ax^3 + bx^2 + cx + d. We are given three points (-2, 3), (3, -7), and (-7, -20) that lie on the graph of the cubic function.
We can substitute these values into the equation and solve for a, b, c, and d to find the specific cubic function that passes through these points. By substituting these values and solving the system of equations, we get the cubic function y = -0.5x^3 - 3x^2 - 2.5x - 3.