(a)On the same coordinate axes, sketch graphs (as accurately as possible) of the functions
\[
y=x^{3}-7 x^{2}+5 x+3 \text { and } y=-4 x^{2}+15 x+3
\]
(b) Find the coordinates of all intersection points. (Enter your answer as a list of ordered pairs, e.g., $(1,2),(3,4), \ldots)$

Step 1 ：First, we need to find the intersection points of the two functions, which means we need to solve the equation $x^{3}-7 x^{2}+5 x+3 = -4 x^{2}+15 x+3$.

Step 2 ：Rearranging the equation, we get $x^{3}-3 x^{2}-10 x = 0$.

Step 3 ：The roots of this equation are the x-coordinates of the intersection points. By Vieta's formulas, the sum of the roots is equal to the coefficient of $x^{2}$ in the equation, which is $-3$.

Step 4 ：Substitute the roots into the equation $y=-4 x^{2}+15 x+3$ to get the y-coordinates of the intersection points. The sum of the y-coordinates is $-4(-3)+15+3=18$.

Step 5 ：Hence, the ordered pair $(A,B)$ is \(\boxed{(-3,18)}\).