The graphs below have the same shape. what is the equation of the red graph?

we have

the vertex of the function g(x) is the point

the vertex of the function f(x) is the point

so

the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

that means

the translation is units down

therefore

the equation of the function f(x) is

therefore

the answer is

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

look a the sides they are perpendicular