Final answer:
The y-intercept of the polynomial f(x)=-6-x³-9x²+3x is -6, which is the point where the graph intersects the y-axis at (0, -6).
Step-by-step explanation:
The y-intercept of a polynomial is found by evaluating the polynomial when x is zero. In this case, for the polynomial f(x)=-6-x³-9x²+3x, we will substitute x with 0 and simplify to find the y-intercept.
So, f(0) = -6 - (0)³ - 9*(0)² + 3*(0) = -6. Hence, the y-intercept of the polynomial is -6.
This means that the point where the graph of the polynomial intersects the y-axis is (0, -6).