If the vertex of the parabola y = - x ^ - 2x + P is on the straight line y = x / 2-1, find the value of P, and then change the parabola expression to the form of y = a (x + m) ^ + K Process!

If the vertex of the parabola y = - x ^ - 2x + P is on the straight line y = x / 2-1, find the value of P, and then change the parabola expression to the form of y = a (x + m) ^ + K Process!

y=-(x+1)^2+p+1
So vertex coordinates (- 1, P + 1)
Substituting into the straight line, we can get P = 2.5
y=-(x+1)^2+3.5

It is known that the vertex coordinates of the quadratic function y = - 1 / 2 times the square of (x-m) + the square of M-4 are in Zhixian y = 2x + 4, the expression of this parabola

The vertex coordinates (m, m ^ 2-4), which are on the line y = 2x + 4, are substituted, and the solution is m = 4 or - 2
When m = 4, the function y = - 1 / 2x ^ 2 + 4x + 4
When m = - 2, the function y = - 1 / 2x ^ 2-2x-2

There is only one common point between the straight line passing through the point (- 3,2) and the parabola y2 = 4x

Let the linear equation be: y = K (x + 3) + 2, and substitute it into the parabolic equation to get k2x2 + (6k2 + 4k-4) x + 9k2 + 12K + 4 = 0 (*). If k = 0, y = 2, which is consistent with the meaning of the problem; if K ≠ 0, △ = (6k2 + 4k-4) 2-4k2 (9K