The equation of the function that could make the graph is f(x) = x²(x - 2)²(x - 4)²
How to determine the function of the graph
From the question, we have the following parameters that can be used in our computation:
The graph
Taking the relative maxima as the zeros of the graph, we have the following
Zeros: x = 0, 2 and 4
Where the zeros have a multiplicity of 2 each
This is so because the graph touches (but not cross) the x-axis at this point
So, we have the expression in factored form to be
f(x) = x²(x - 2)²(x - 4)²
Hence, the expression in factored form is f(x) = x²(x - 2)²(x - 4)²