Given that the parabola y = - 3x & # 178; + BX + C passes through points (3,1) and (0,4), then the value of B + C is?

Given that the parabola y = - 3x & # 178; + BX + C passes through points (3,1) and (0,4), then the value of B + C is?

C = 4, B = 8

It is known that the parabola far y = 1 / 3x & # 178; + BX + C intersects the x-axis at point a (- 3,0) and the y-axis at point E (0,1)
Question: (1) find the analytic expression of this quadratic function
(2) If the point Q (m, n) is on this parabola and - 3 ≤ m < 3, the value range of n is obtained
(3) Let point B be another intersection point of this parabola and X axis, and p be a moving point on the parabola different from point B. connect BP to intersect Y axis at point n (point n is above point E). If △ AOE ∽ Bon, calculate the coordinates of point P

1. Substituting points a and E, we can get C = 1, B = 4 / 3, then y = 1 / 3x & # 178; + 4 / 3x + 1
2. The function can be reduced to y = 1 / 3 (x + 2) Square-1 / 3
Nmin = - 1 / 3, M = 3jf, n = 8, so - 1 / 3 ≤ n < 8
3. Because △ AOE and bo have been determined, it seems that there are two cases: n (0,3) and (0 ', 1 / 3) can be obtained according to the similar proportional relationship, and n (0,3) can be obtained because n is above E
Then the line NB is y = 3x + 3
The equations formed with parabola are: P (6.21) P (- 1,0) rounding off