If the vertex of the parabola y = - x square - 2x + P is on the straight line y = x / 2-1, find the value of P, and then rewrite the expression of the parabola into the form of y = a (x + m) square + K | Math enthusiast | Mathematical art

If the vertex of the parabola y = - x square - 2x + P is on the straight line y = x / 2-1, find the value of P, and then rewrite the expression of the parabola into the form of y = a (x + m) square + K

Let their intersection be a, then the relation between X and y of a satisfies both linear equation and parabolic equation
Let a parabola have a vertex formula
Ax square + BX + C = y
The abscissa of the vertex is - B / 2A,
The ordinate value is (4ac-b Square) / 4A
So a (- 1, (- 4p-4) / - 4) is substituted into the linear equation
（-4p-4）/-4=-0.5-1
p=0.5
Y = - 2x + 0.5
Y = - 2x-1 + 1 + 0.5
Y = - (x + 1) square + 1.5

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