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

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)