Question 916703
p is a fourth degree polynomial, but you only have 3 roots. So one root has to be repeated (you need 4 total roots).


The y-intercept is -2, so that means p(0) = -2


So you may have p(x)= k(x-1)^2(x-4)(x-10) or p(x)= k(x-1)(x-4)^2(x-10) or p(x)= k(x-1)(x-4)(x-10)^2


Let's see what happens with p(x)= k(x-1)^2(x-4)(x-10)


p(x)= k(x-1)^2(x-4)(x-10)


p(0)= k(0-1)^2(0-4)(0-10)


-2 = 40k


40k = -2


k = -2/40


k = -1/20


So the function is {{{p(x) = expr(-1/20)(x-1)^2(x-4)(x-10)}}}


This graph (in green) confirms it


{{{ graph( 500, 500, -5, 15, -30, 30, 0,(-1/20)(x-1)^2(x-4)(x-10)) }}}



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Thanks,


Jim