Final answer:
To find the y-intercept of the function f(x) = -(x-3)^2(x+4), set x=0 and solve for y, which results in y = -36. Hence, the y-intercept is the point (0, -36).
Step-by-step explanation:
The student has asked to find the y-intercept of the function f(x) = -(x-3)2(x+4). To find the y-intercept of a function, we substitute x = 0 into the equation and calculate the corresponding y value. In this case:
- f(0) = -(0-3)2(0+4)
- f(0) = -9 × 4
- f(0) = -36
Therefore, the y-intercept of the function is -36, which means the graph of this function crosses the y-axis at the point (0, -36).