Quadratic equation of one variable from the point of view of function It is known that the image of quadratic function y = x ^ 2 - (M + 1) x + m intersects two points a (x1,0) and B (x2,0), the positive half axis of intersection Y axis is at point C, and X1 ^ 2 + x2 ^ 2 = 10; (1) Find the analytic expression of quadratic function; (2) Whether there is a straight line passing through point d (0,2.5) intersecting with parabola and points m, n intersecting with X axis at point E, so that points m, n are symmetrical with respect to point E. if there is, the analytical expression of straight line Mn is obtained. If not, the reason is explained
(1) X1 ^ 2 + x2 ^ 2 = (x1 + x2) ^ 2-2x1 * x2 = m ^ 2 + 2m + 1-2m = 10 m = positive and negative 3 intersection Y axis positive half axis
At point C, M = 3
y=x^2-4x+3
Let: the linear Mn equation be y = KX + 2.5, e (2.5 / K, 0), m (x1, Y1), n (X2, Y2)
x2+x1=5/k
y1=x1^2-4x1+3
y2=x2^2-4x2+3
y2-y1=(x2-x1)(x2+x1)-4(x2-x1)
K = 5 / K-4, k = - 1 or K = 5 (rounding off)