It is known that the quadratic function y = x square - (m square + 4) x-2m square-12 1. Verification: no matter what real number m takes, the parabola passes through a certain point, and the coordinates of the fixed point are obtained

It is known that the quadratic function y = x square - (m square + 4) x-2m square-12 1. Verification: no matter what real number m takes, the parabola passes through a certain point, and the coordinates of the fixed point are obtained

Let: y = x ^ 2 - (m ^ 2 + 4) x-2m ^ 2-12 = 0, the discriminant: [- (m ^ 2 + 4)] ^ 2-4 (- 2m ^ 2-12) = m ^ 4 + 8m ^ 2 + 16 + 8m ^ 2 + 48 = m ^ 4 + 16M ^ 2 + 64 = (m ^ 2 + 8) ^ 2, because m ^ 2 is greater than or equal to 0, so m ^ 2 + 8 is greater than 0, that is, the discriminant is greater than 0, indicating that the equation has two unequal real roots, that is, there must be two intersections with the X axis