Given that the image of the function y = (m-2) x square - 3x + m square + 2m-8 of Y with respect to x passes through the origin, the analytic expression of the function is obtained

Given that the image of the function y = (m-2) x square - 3x + m square + 2m-8 of Y with respect to x passes through the origin, the analytic expression of the function is obtained

Because: the image of y = (M - 2) x ^ 2 - 3x + m ^ 2 + 2m - 8 passes through the origin,
So: when x = 0, y = 0
Substitute x = 0, y = 0 into the above function expression to get
m^2 + 2m - 8 = 0
To solve the equation about M, M = 2, or M = - 4
Because it is a quadratic function, so (M - 2 ≠ 0), that is, m ≠ 2
Substitute M = - 4 into the above function expression to get y = - 6x ^ 2 - 3x
This is the analytic expression of the function