In y = ax & # 178; + BX + C, the solution of A0 is? Ax & # 178; + BX + C

The solution of A0, between a and B, is - 1 < x < 2
ax²+bx+c

It is known that the intersection of y = ax & # 178; + BX + C and X axis is a (1,0), B (3,0)
The point of intersection with y axis is C, and the vertex is d. if the surface of quadrilateral ABCD is 18, find the analytical formula of parabola? The respondent should write the detailed points as much as possible
A (negative 1, 0) has the wrong number

Connecting OD, let C (0, c), D (1, m), the analytic formula of parabola be y = a (x + 1) (x-3) = a (x-1) ^ 2-4a
Then C = - 3a,
When the parabolic opening is upward, the area of quadrilateral ABCD is s = - C / 2 + (- C) + - 3M) / 2 = 18,
M = - C-12, so - 4A = - C-12, a = 12 / 7;
When the opening of parabola is downward, a = - 12 / 7 can be obtained
The analytical formula of the parabola is y = 12 / 7 (x + 1) (x-3) or y = - 12 / 7 (x + 1) (x-3)

What is the symmetry axis of parabola y = ax & # 178; + BX + C? What is the vertex coordinate?

y=a(x+b/2a)²+ (4ac-b²)/4a
The axis of symmetry is x = - B / 2A
The vertex coordinates are (- B / 2a, (4ac-b & # 178;) / 4A)

It is known that the abscissa of the intersection point of the parabola y = AX2 + BX + C and X axis is - 1 and 2 respectively, and it passes through the point (3, 8). The analytical formula of the parabola is obtained

Let the analytical formula of parabola be y = a (x + 1) (X-2), substituting the point (3, 8) to get, 8 = 4A, the solution is a = 2, so the analytical formula of parabola is y = 2 (x + 1) (X-2), that is, y = 2x2-2x-4

In y = ax & # 178; + BX + C, the solution of A0 is? Ax & # 178; + BX + C