(1) Find the expression of this parabola;
(2) point q is on the y axis and point p is on the parabola. Let a quadrilateral with Q, P, A and B as vertices be a parallelogram, and find the coordinates of all points P that satisfy the conditions.
Test answer:
Solution: (1) Let the expression of this parabola be y=ax? According to the meaning of the question, you must
Solve it and get it.
The expression of parabola is y=x? -x- 1
(2) When AB is an edge, as long as PQ∨AB and PQ=AB=4.
It is also known that point Q is on the Y axis, and the abscissa of point P is 4 or -4. At this time, there are two qualified points p, which are marked as P 1 and P2 respectively.
And when x=4, y =；; When x=-4 and y=7,
At this time, P 1(4,) P2(-4, 7).
② When AB is diagonal, as long as PQ line and AB line are equally divided.
It is also known that point Q is on the Y axis, and the abscissa of the midpoint of line segment AB is 1.
The abscissa of point p is 2. At this time, only one qualified P is recorded as P3.
And when x=2, y=- 1, P3(2,-1).
To sum up, the qualified p is P 1(4,) p2 (-4,7) P3 (2,-1).