help write the equation for the graph

Question

for the given graph at x = 1, 2, and 4 since these are the x-intercepts and where the function would equal zero. Both at 1 and at 2, the multiplicity has to be odd, since the function crosses straight through the x-axis. At x = 4, the multiplicity is even since the graph turns around. Given the number of curves or turning points- which looks to be three- the total of the exponents should add up to four (one more than the number of curves). So, the multiplicity at 1 and 2 is one, while at 4 it is actually two. For part b) write an equation, express as the product of factors, of a polynomial function for the graph. Use a leading coefficient of 1 since the graph is pointing up on both ends. Make the degree of f as small as possible which means to use each zero only as many times as indicated by the part (a).

Answer 1

f(x)=(x-1)(x-2)(x-4)²

since the leading coefficient is 1, there is no need to put a number in front of the parentheses.

Since we want the degree as small as possible, we use degree 1 for odd and degree 2 for even.