Question

What is the vertex of `y=5(x/3-15)^2-4`?

Answer 1

Vertex `(45,-4)`

Explanation:

There are a couple ways of doing this; perhaps the most obvious is to convert the given equation into standard vertex form:
`color(white)("XXX")y=m(x-a)^2+b` with its vertex at `(a,b)`

`y=5(x/3-15)^2-4`

`rarr y=5((x-45)/3)^2-4`

`rarr 5/9(x-45)^2+(-4)`
`color(white)("XXX")`which is the vertex form with vertex at `(45,-4)`

Alternately think of replacing `hatx=x/3` and the given equation is in vertex form for `(hatx,y)=(15,-4)`
and since `x=3*hatx` the vertex using `x` is `(x,y)=(3xx15,-4)`
graph{5(x/3-15)^2-4 [35.37, 55.37, -6.36, 3.64]}