In a quadratic equation y=d(x-a)^b+c(assuming b>1)?

Question

Linear equation y=ax+b, would b have a vertex if b=3?

Answer 1

you are recycling 'parameters' here.
in your linear equation b is a y-intercept.
Otherwise, you intend b to be a power.

If b is not 2, it is not a quadratic equation.

Still, following your intention, say if b = 3,
y=d(x-a)^3 + c will not have a vertex (local extremum) at a, it will have a point of inflection.

d:

Answer 2

I am not sure what you are asking about. But the closest I can think of is if b=3 then the graph is that of a cube curve which generally looks like an S with no vertex.