We can use the standard form of the quadratic function, which is f(x) = ax^2 + bx + c, to write an equation for this function.
First, we can find the value of "a" by using the fact that the function is quadratic. We know that the second differences between the values of f(x) are constant, which means that a = 1/2(16 - 2(15) + 12) = -1/2.
Next, we can use the point (0, 15) to find the value of "c". Plugging in x = 0 and f(x) = 15, we get:
15 = (-1/2)(0)^2 + b(0) + c
So c = 15.
Finally, we can use another point, such as (-4, 12), to find the value of "b". Plugging in x = -4 and f(x) = 12, we get:
12 = (-1/2)(-4)^2 + b(-4) + 15
Simplifying this equation, we get:
12 = 8 - 4b + 15
-11 = -4b
b = 11/4
Putting it all together, we get the equation:
f(x) = -1/2x^2 + 11/4x + 15