can someone please help me?
show an equation that represents the polynomial function with zeros –1, 1, and 3 (multiplicity of 2), and a y-intercept of –18?

Question

can someone please help me?
show an  equation that represents the polynomial function with zeros –1, 1, and 3 (multiplicity of 2), and a y-intercept of –18?

misty1212 · Answer

HI!!

misty1212 · Answer

since you know the zeros you can write it in factored form

misty1212 · Answer

since $-1$ is a zero, one of the factors has to be $x+1$ and so on

misty1212 · Answer

multiplicity 2 means the exponent on the $x-3$ factor is $2$ so you can start with $$a(x+1)(x-1)(x-3)^2$$

misty1212 · Answer

you still need $a$ however, but that is not hard 
since the y intercept is -18 replace $x$ by $0$ and set the result equal to $-18$ and solve for $a$ , i.e. solve $$a(1)(-1)(-3)=-18$$