Use the factored form, one factor for each zero:
y = a(x-3)2(x-1)(x+2)
The double zero at x = 3 means to square that factor. The coefficient a can be found using the given point (0,12):
y = a(x-3)2(x-1)(x+2)
12 = a(0-3)2(0-1)(0+2)
12 = a(9)(-1)(2)
12 = a·(-18)
12/(-18) = a = -2/3
The full polynomial is:
y = (-2/3)(x-3)2(x-1)(x+2)
Multiply it out to put it into standard form.
Philip P.
tutor
No it's good question. Each factor, needs to equal zero for the specified x values. So if -2 is given as a zero for x, then the factor is (x+2) because when I put in -2 for x, I get (-2 + 2) = 0. So the number added to x has the opposite sign.
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03/09/18
Tara S.
03/09/18