In the function f (x) = ax ^ 2 + BX + C, if a, B, C are in equal proportion sequence and f (0) = - 4, then f (x) has a. Maximum 3 b. Minimum 3 c. Maximum - 3 d. Minimum - 3

In the function f (x) = ax ^ 2 + BX + C, if a, B, C are in equal proportion sequence and f (0) = - 4, then f (x) has a. Maximum 3 b. Minimum 3 c. Maximum - 3 d. Minimum - 3

a. B, C are equal ratio sequence and f (0) = - 4
Let B = cm, a = cm ^ 2
therefore
f(0)=c=-4
b=-4m
a=-4m^2
f(x)=-4m^2x^2-4mx-4=-(2mx-1)^2-3
Then when x = 1 / 2m
F (x) has a maximum value of - 3

The function f (x) = ax ^ 2 + BX + C, X ∈ R, if a, B, C are equal ratio sequence, and f (0) = - 4, then the range of function f (x) is

From a, B, C into a series of equal proportion, B & sup2; = AC, and B ≠ 0; from F (0) = - 4, C = - 4, the two are simultaneous
a=(-1/4)b²,c= -4,
So f (x) = (- 1 / 4) B & sup2; X & sup2; + bx-4 (B ≠ 0)
The coefficient of quadratic term is less than 0, so f (x) has a maximum, which can be calculated as - 3
The range is (- ∞, - 3)

Given the quadratic function f (x) = ax ^ 2 + BX + C (1), if a > b > C and f (1) = 0, it is proved that the image of F (x) and X axis have two different intersections; (2) it is proved that if x 1, x 2 and x 1 are the same, the image of F (x) has two different intersections

【1】 Let g (x) = f (x) - [f (x1) + F (x2)] / 2, then: G (x1) = [f (x1) - f (x2)] / 2, G (x2) = [f (x2) - f (x1)] / 2, because f (x1) ≠ f (x2), then: [g (x1)] × [g (x2)]