The parabola y = AX2 + BX + 3 intersects with the X axis at points a (1,0) and B (- 3, O), and intersects with the Y axis at point C (1). Find the analytical formula of the parabola (2) let the symmetry axis of the parabola and X

The parabola y = AX2 + BX + 3 intersects with the X axis at points a (1,0) and B (- 3, O), and intersects with the Y axis at point C (1). Find the analytical formula of the parabola (2) let the symmetry axis of the parabola and X

(1) From the problem, we know that the two equations ax ^ 2 + BX + 3 = 0 are 1, - 3 respectively, so we can get: 1 + (-- 3) = -- B / a 1 * (-- 3) = 3 / A from WIDA's theorem. From this solution, we can get: a = -- 1, B = -- 2, so we can get

The image of parabola y = AX2 + BX + C (a > 0) passes through points B (12,0) and C (0, - 6), and the axis of symmetry x = 2

Substituting B (12,0), C (0, - 6) into function
0=a*12^2+12b+c...(1)
-6=c.(2)
From the symmetry axis X = 2, - B / 2A = 2.. (3)
From the above, we can get: a = 1 / 16, B = - 1 / 4, C = - 6
y=1/16X^2-1/4x-6

In the plane rectangular coordinate system xoy, make a straight line passing through the point P (0,2) which intersects with the parabola y = AX2 (a > 0) at two points. If the intersection is a and B, then the product of the ordinates of a and B is______ ．

Let a (x1, Y1), B (X2, Y2), and X1 < X2, then X1 and X2 are the two real roots of equation ③. So X1 + x2 = Ka, x1 ·x2 = - 2A, so Y1 ·y2 = ax21 ·ax22 = A2 · (x1 ·x2) 2 = A2 · (- 2A) 2 = 4;

In the plane rectangular coordinate system xoy, the parabola y = - 1 / 2x ^ 2 + BX + C passes through points a (1,3), B (0,1)
Take a point P on the y-axis to make △ ABP similar to △ ABC, and find all P satisfying the condition

In the title: (1) y = (x + 1) (x + 3) = x ^ 2 + 4, x + 3 start = x ^ 2 + BX + C, so B = 4, C = 3. Y = x ^ 2 + 4, x + 3 start (2) sin = sin. = 2 (103 / root, 10-1 / square root) = 1 / 5, let P (a, 0) sin = 1 / root (a ^ 21) = 1 / 5