Be ax^2+bx+c. Knowing f(1) = 4, f(2) = 0 and f(3) = -2 calculate the product abc.

Expert Answers
lfryerda eNotes educator| Certified Educator

We need to use the given information by substituting the x-values into the function `f(x)=ax^2+bx+c` .

`f(1)=4=a+b+c`   equation (1)

`f(2)=0=4a+2b+c`    equation (2)

`f(3)=-2=9a+3b+c`   equation (3)

Now we need to solve the three equations for the three unknowns.

(2)-(1) gives `3a+b=-4`  equation (4).

(3)-(2) gives `5a+b=-2` equation (5).

(5)-(4) gives `2a=2` which means a=1.

Sub in (4) to get: 

`3+b=-4`  so b=-7

Now sub in (1) to get:

`1-7+c=4` which means c=10.

The product is `abc=(1)(-7)(10)=-70` .