The known function f (x) = x2 + 2aX + 3, X ∈ [- 4,6] When a = 1, find the monotone interval of F (| x |) When a = 1, f (x) = x2 + 2x + 3, If f (| x |) = x2 + 2 | x | + 3, then the definition field is x ∈ [- 6,6]. I don't understand why the definition field is [- 6,6]. The main premise is not that the definition field is [- 4], but I haven't figured it out for a long time,

The known function f (x) = x2 + 2aX + 3, X ∈ [- 4,6] When a = 1, find the monotone interval of F (| x |) When a = 1, f (x) = x2 + 2x + 3, If f (| x |) = x2 + 2 | x | + 3, then the definition field is x ∈ [- 6,6]. I don't understand why the definition field is [- 6,6]. The main premise is not that the definition field is [- 4], but I haven't figured it out for a long time,

F (| x |) = x2 + 2 | x | + 3, at this time | x |, is the same as the range of X in the original function, that is | x | ∈ [- 4,6], so the domain of definition is x ∈ [- 6,6]

The vertex coordinate formula of parabola y = ax & # 178; + BX + C~

y＝ax²+bx+c
=a(x+b/2a)²+(4ac-b²)/4a
So the vertex coordinates are (- B / 2a, (4ac-b & # 178;) / 4A)
If you don't understand, I wish you a happy study!

The image of parabola y = - 2x2 + 8x-1 is rotated 180 ° around the origin, and the vertex is translated downward, just intersecting with the straight line y = KX + 2 at the point (3,5), so as to find a new parabola
Line analytic expression

y=2x2+8x-37

It is known that a = {x 2-5x + 4 ≤ 0}, B = {x 0}

This paper is a 8746; B = (0,4) a 8745; B = [1,2] a ∩ cub = [2,4] CUA ∩ cub = [2,4] CUA [2,4] CUA ∩ cub = (- ∞, 0] 8746 (4, + (4, (4, + ∞) process: \\\\\\\ (4 (4 87464646464646\\8746;\\\\\\\8746;\\\\\\\\4, +