Functiong is a transformation of the parent quadratic function f. Which statements are true about this function? g(x) = -(x - 4)^2+ 6
Select all the correct answers.
A. Function g reflected function f across the x-axis
B. Function g translated the vertex from(0,0) to (-4,6)
C. For function g, as x approaches negative infinity, g(x) approaches negative infinity.
D. Function g is always decreasing.
E. Function g is always negative.
G. Function g is symmetrical about the point (4,6).

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0