There is such a problem: "the quadratic function y = AX2 + BX + C is known to pass P (1, - 4), and C = - 3a To prove the image of this quadratic function, we must pass the fixed point a (- 1,0) Can you find the quadratic function expression according to the information in the question? If you can, please ask; if you can't, please explain the reason; (2) according to the existing information, please Add an appropriate condition to complete the original question

There is such a problem: "the quadratic function y = AX2 + BX + C is known to pass P (1, - 4), and C = - 3a To prove the image of this quadratic function, we must pass the fixed point a (- 1,0) Can you find the quadratic function expression according to the information in the question? If you can, please ask; if you can't, please explain the reason; (2) according to the existing information, please Add an appropriate condition to complete the original question

(1) According to the meaning of the problem, we can get: - 4 = a + B + CC = - 3A0 = A-B + C, the solution is a = 1b = - 2C = - 3, y = x2-2x-3; (2) add the condition: the symmetry axis line x = 1 (not unique)

Quadratic function y = ax ^ 2 + BX + C, P = / A-B + C / + / 2A + B /, q = / A + B + C / + / 2a-b /, find the size relationship of P and Q
/The sign a + B + C / is absolute
The graph opening of quadratic function y = ax ^ 2 + BX + C is downward, and the symmetry axis is on the right side of Y axis

Opening downward = > a C = 0
On the right side of y-axis = > - B / 2A > 1 = > 0