We know the quadratic function y = x ^ 2-mx-4. (1) prove that the image of the function must have two different intersections with the X axis; (2) let the coordinates of the intersection of the image of the function and the X axis be (x1,0), (x2,0), and 1 / X1 + 1 / x2 = - 1, find the value of M, and find the vertex coordinates of the function image. (please answer with junior high school mathematics knowledge)

We know the quadratic function y = x ^ 2-mx-4. (1) prove that the image of the function must have two different intersections with the X axis; (2) let the coordinates of the intersection of the image of the function and the X axis be (x1,0), (x2,0), and 1 / X1 + 1 / x2 = - 1, find the value of M, and find the vertex coordinates of the function image. (please answer with junior high school mathematics knowledge)

(1)Δ=b²-4ac=(-m)²-4×1×-4=m²+16
∵m²≥0
∴m²+16 ≥0
The quadratic function y = x ^ 2-mx-4 has two different intersections with the X axis
（2）1÷x1+1÷x2=-1
（x1+x2）÷（x1×x2）=-1①
∵ when the intersection coordinates of quadratic function and X axis are (x1,0), (x2,0)
When x ^ 2-mx-4 = 0, the solution of the equation is x1, x2
According to the relationship between the root and coefficient of quadratic equation of one variable
x1+x2=-b÷a=m
x1×x2=c÷a=-4
By substituting X1 + x2 = m, x1 × x2 = - 4 into formula (1), we get
m÷-4=-1
m=4
Substituting M = 4 into quadratic function y = x ^ 2-mx-4
y=x²-4x-4
y=x²-4x+4-4-4
y=(x-2)²-8
The vertex coordinates (2, - 8)