Final answer:
The y-coordinate of the y-intercept of the polynomial f(x) = -2(4x² +4)(x-5)(x+1) is 40.
Step-by-step explanation:
The y-intercept of a polynomial is the point where the polynomial intersects the y-axis. In order to find the y-coordinate of the y-intercept for the given polynomial f(x) = -2(4x² +4)(x-5)(x+1), we need to substitute x=0 into the polynomial and evaluate the corresponding y-value.
Let's plug in x=0 into the polynomial: f(0) = -2(4(0)² +4)(0-5)(0+1) = -2(4)(-5)(1) = 40
Therefore, the y-coordinate of the y-intercept is 40.