There is a quadratic function image, three students respectively said some of its characteristics: A: the axis of symmetry is a straight line, x = 4; B: the abscissa of the intersection with the X axis is an integer C: the point of intersection with the Y axis is also an integer, and the area is 12

There is a quadratic function image, three students respectively said some of its characteristics: A: the axis of symmetry is a straight line, x = 4; B: the abscissa of the intersection with the X axis is an integer C: the point of intersection with the Y axis is also an integer, and the area is 12

Let the analytic formula be y = a (x-x1) (x-x2), and let X1 < X2, then the intersection of the image and the Y axis is a (x1,0), B (x2,0), and the coordinates of the intersection of the image and the Y axis are (0, ax1x2); ∵ the symmetric axis of the parabola is a straight line x = 4, ∵ x2-4 = 4 - x1, that is: X1 + x2 = 8 ∵ s ∵