Write an analytic expression of quadratic function, so that its image satisfies two conditions The vertex is on the line y equals - X Without going through the origin, the analytic expression of this quadratic function can be?

Write an analytic expression of quadratic function, so that its image satisfies two conditions The vertex is on the line y equals - X Without going through the origin, the analytic expression of this quadratic function can be?

If the vertex is y = - x, we can set the vertex as (h, - H), let y = a (X-H) ^ 2-h
If x = 0, y = ah ^ 2-h ≠ 0, if h ≠ 0, then a ≠ 1 / h
For example, y = 2 (x-1) ^ 2-1