Final answer:
To write a function that has constant second differences, first differences that are not constant, a y-intercept of 2, and passes through the point (-16,3), we can use a quadratic function. By substituting the given point into the function and solving for the coefficients, we can find the specific function that meets the requirements.
Step-by-step explanation:
To write a function that has constant second differences, first differences that are not constant, a y-intercept of 2, and passes through the point (-16,3), we can use a quadratic function. A quadratic function is in the form y = ax^2 + bx + c. Since we want constant second differences, the coefficient of x^2 should be 0. To find the coefficients a, b, and c, we can substitute the given point into the function and solve for the coefficients.
Given the point (-16,3), we have 3 = a(-16)^2 + b(-16) + c. Plugging in the value of x and y into the equation, we get 3 = 256a - 16b + c. Since we want the y-intercept to be 2, we have c = 2. Substituting c = 2 into the equation, we have 3 = 256a - 16b + 2. Simplifying the equation, we get 1 = 256a - 16b. Since we want first differences that are not constant, we can choose any values for a and b as long as they satisfy the equation. For example, we can choose a = 1 and b = -15.
Therefore, the function that satisfies the given conditions is y = x^2 - 15x + 2.