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Question:

I need your help~~

Find an expression for a cubic function f iff(1) = 12 and f(-3) =f(0) = f(2) = 0.

f(x) =

ANSWER

Find an expression for a cubic function

f if f(1) =12 and f(-3) = f(0) = f(2) = 0.

f(x) =  ax3  +bx2+cx+ d

f(1) = 12  ==> a(1)3  +b(1)2 + 1 c + d    = 12

f(-3)= 0 ==> a(-3)3  +b(-3)2  -3  c + d   =  0

f(0) = 0  ==> 0+0+0+ d    =  0   ==>d=0

f(2) = 0  ==> a(2)3  +b(2)2  +2  c + d   =  0

Solve[{a+b+c+d==12,

a*(-3)^3+b*(-3)^2-3*c+d==0,

d==0,

a*(2)^3+b*(2)^2+2*c+d==0

},{a,b,c,d}]

a=-3,

b=-3,

c=18,

d=0

f(x) = -3x3  -3 x2 +18x+ 0  ANSWER