The first problem is to get the coordinates of A and B first, and then get the analytical formula of quadratic function by the method of undetermined coefficient.
Solution: (1) A(0, 1) and B(-3, 5/2) can be found in the title. According to the meaning of the title, C = 1, 9a-3b+C = 5/2, and A-b+C = 4. The detailed answer is here. And it intersects with the straight line y=- 1/2x+ 1 at two points A and B (as shown in the figure). Point A is on the Y axis, point B is BC perpendicular to the X axis, and point C (-3,0) is the vertical foot.
I hope I can help you. Come on, I wish you progress in your study ...