The intersection of the parabola Yax & # 178; + BX + C (a > 0) and the x-axis is a (x1,0), B (x2,0). The solution set of X10 is the inequality ax & # 178; + BX + C < 0?

The intersection of the parabola Yax & # 178; + BX + C (a > 0) and the x-axis is a (x1,0), B (x2,0). The solution set of X10 is the inequality ax & # 178; + BX + C < 0?

The solution set of ax & # 178; + BX + C > 0 (- ∞, x1) U (x2. + ∞) ax & # 178; + BX + C < 0 (x1, x2)

The two roots x1, X2 (x1 < x2) of the quadratic equation x2 + 2x-3 = 0 are the intersection of the parabola y = AX2 + BX + C and the X axis

1. Substituting the point C (0,1) into y = ax ^ 2 + BX + C, we can get C = 1; X1 and X2 are the two roots of the equation AX2 + BX + C = x, so X1 + x2 = - (B-1) / A, and X1 = - X2, so X1 + x2 = 0,

As shown in the figure, the parabola y = AX2 + BX + C passes through three points a (- 3.0) B (1.0) C (3.6) and intersects with the Y axis at point E
1. Find the analytical formula of parabola
2. If the coordinate of point F is (0. - 1 / 2) the intersection parabola of straight line BF and another point P, try to compare the perimeter of triangle AFO and triangle PEF, and explain the reason
AB is on the x-axis and E is on the negative half axis of y-axis

As shown in the figure, the parabola y = AX2 + BX + C is substituted by a (- 3.0) B (1.0) C (3.6) to get 9a-3b + C = 0A + B + C = 09A + 3B + C = 6A = 1 / 2 b = 1 C = - 3 / 2 Desorption formula y = x2 / 2 + x-3 / 2 (2) if the coordinate of point F is (0. - 1 / 2) BF intersection parabola and another point PE (0, - 3 / 2) suppose the analytic formula of BF line y = ax + Ba + B = 0b

It is known that the image of the quadratic function y = ax + B passes through the point (- 2,1). For the parabola y = ax ^ 2-bx + 3, there is the following statement:
① Over point (2,1)
② The axis of symmetry can make the line x = 1
③ When a ＜ 0, the minimum value of the ordinate of the fixed point is 3, and the correct ones are ① right and ② wrong. I know the reasons for these two, but why is the third one right? Please prove that the solution on the Internet is either wrong or wrong with the theorem I haven't learned

Change the parabolic equation to y = a (X-B / 2a) ^ 2 + 3-B ^ 2 / (4a ^ 2)
So the ordinate of the vertex is 3-B ^ 2 / (4a ^ 2)
Since both B ^ 2 and a ^ 2 are definitely nonnegative, the maximum value of the vertex's ordinate is 3.5 when B = 0 and a = - 0.5
So ③ is wrong