Question

which of the following cubic functions has a point of inflection of (6, -8)? (1 point)
○ ( y=-3(x + 6)^{3}-8 )
○ ( y=2(x - 6)^{3}-8 )
○ ( y=5(x - 6)^{3}+8 )
○ ( y=2(x + 6)^{3}+8 )

Explanation:

Step1: Recall the form of a cubic function

The general form of a cubic function with a point of inflection \((h,k)\) is \(y = a(x - h)^{3}+k\).

Step2: Substitute the given point \((h = 6,k=-8)\)

Substituting \(h = 6\) and \(k=-8\) into the general form, we get \(y=a(x - 6)^{3}-8\).

Answer:

\(y = 2(x - 6)^{3}-8\) (the second option)