(2) net income g = x months of total profit - total investment of 1.5 million - x months of repair and maintenance costs, can be simplified to find the analytic formula of g on x;
(3) first with the method of the analytic formula for the apex of the formula to obtain the apex coordinates of the problem of its maximum value; only when g > 0 can recover the investment; only when g > 0 can recover the investment; only when g > 0 can recover the investment. Can know the maximum value of the problem; only when g>0, can recover the investment, so according to the quadratic function g>0 when the corresponding value of x to determine its in the sixth month can recover the investment. Answer: Solution: (1) According to the meaning of the question can be seen
when x = 1, y = 2,
when x = 2, y = 6,
so a + b = 24a + 2b = 6,
Solve a = 1b = 1,
∴ y = x2 + x;
(2) the net income g = 33x-150 - (x2 + x) ,
=-x2+32x-150;
(3) g=-x2+32x-150=-(x-16)2+106,
that is, the net income of the amusement park is maximized after the facility has been open for 16 months.
And in 0 When x ≤ 5, g <0; And when x = 6, g>0, So the investment can be recovered after 6 months. Comment: The main test uses the model of quadratic function to solve practical problems. First according to the meaning of the problem to find the analytic formula of the quadratic function is the key to solving the problem. To find the maximum value of the problem can be solved by using the coordinates of the vertex of the parabola.