Translate the parabola y = x ^ 2 + BX + C three unit lengths to the left, and then translate it two unit lengths to the upper, then get the parabola y = x ^ 2 + 3x + 6, and find the values of B and C

Translate the parabola y = x ^ 2 + BX + C three unit lengths to the left, and then translate it two unit lengths to the upper, then get the parabola y = x ^ 2 + 3x + 6, and find the values of B and C

Simple method: the translation of parabola can be regarded as the translation of symmetry axis and vertex
The axis of symmetry of the new parabola is - 3 / 2
The top is 15 / 4
Then the original axis of symmetry should be - 3 / 2 + 3 = 3 / 2
The original vertex is 15 / 4-2 = 7 / 4
That is: - B / 2A = 3 / 2, - B / 2 = 3 / 2, B = - 3
(4ac-b^2）/（4a)=7/4
(4c-9)/4=7/4
c=4
That is, B = - 3, C = 4