The known parabola y = - x square + 2 (k-1) x + K + 2 10 - 14 days and 23 hours to the end of the problem It intersects with X axis at two points AB, and point a is on the negative half axis of X, and point B is on the positive half axis of X Question: (1): find the value range of real number K (2) Let the lengths of OA and ob be a and B respectively, and a: B = 1:5 ,

The known parabola y = - x square + 2 (k-1) x + K + 2 10 - 14 days and 23 hours to the end of the problem It intersects with X axis at two points AB, and point a is on the negative half axis of X, and point B is on the positive half axis of X Question: (1): find the value range of real number K (2) Let the lengths of OA and ob be a and B respectively, and a: B = 1:5 ,

(1) The parabola and X-axis intersect at two points AB, and point a is on the negative half axis of X, and point B is on the positive half axis of X
- x square + 2 (k-1) x + K + 2 = 0, the equation has two different real roots, one positive and one negative,
That is, Δ > 0 and K + 2 / (- 1) - 2;
(2) If y = - (x-k + 1) ^ 2 + K ^ 2-k + 3, then the parabola symmetry axis is x = k-1; the lengths of OA and ob are a, B and a: B = 1:5 respectively, which indicates that (k-1,0) is in the positive semiaxis of X, that is, K > 1, if point a (- A, 0), then point B is (5a, 0)
K-1 - (- a) = 5A - (k-1), - A * 5A = (K + 2) / (- 1), and k > 1;
The solution is k = 3, then the analytic formula is y = - x ^ 2 + 4x + 5