Final answer:
To find the values of a, b, c, and d in the cubic function p(x) = ax + bx^2 + cx + d, we can use the given information of the tangent line and turning point.
Step-by-step explanation:
To find the values of a, b, c, and d in the cubic function p(x) = ax + bx^2 + cx + d, we need to use the given information. We are given that the function has a tangent y = 3x + 1 at the point (0, 1) and a turning point at (-1, -3).
First, let's find the derivative of p(x) to find the slope of the tangent line. The derivative of p(x) is p'(x) = a + 2bx + c. Since the tangent line has a slope of 3, we can set p'(0) = 3 to get a + c = 3.
Next, we can substitute the coordinates of the turning point (-1, -3) into the cubic function to get -3 = -a + b - c + d. With these two equations, we can solve for a, b, c, and d.