A. Math

First I think your question should ask:
The curve y=e^x(ax^2+bx+c) where a, b,c are constants such that its tangent at x=1 and x=3 are parallel to the x-axis, and it cuts the y-axis at y=9. Find a, b and c.

Then the answer is as follow:
Note that y' = e^x(ax^2 + bx + c + 2ax + b) = e^x(ax^2 + (2a +b)x + (b + c))
By the information given in the question, we get
e^0 (0 + 0 + c) = 9, so c = 9
e(a + 2a + b + b + c) = 0, i.e. 3a + 2b + 9 = 0
e^3(9a + 6a + 3b + b + c) = 0, i.e. 15a + 4b + 9 = 0
So solving gives a = 1, b = -6