SOLUTION: A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y - axis at 2. If f(1) = 1, and f(-2)= -2, find f(-1) and write the complete function.

Algebra ->  Rational-functions -> SOLUTION: A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y - axis at 2. If f(1) = 1, and f(-2)= -2, find f(-1) and write the complete function.      Log On


   

Question 1036832: A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y - axis at 2. If f(1) = 1, and f(-2)= -2, find f(-1) and write the complete function.
Found 2 solutions by Fombitz, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
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f%28x%29=-2x%5E3%2Bax%5E2%2Bbx%2Bc
So,
f%282%29=0
-2%282%29%5E3%2Ba%282%29%5E2%2B2b%2Bc=0
-16%2B4a%2B2b%2Bc=0
1.4a%2B2b%2Bc=16
Similarly,
f%281%29=1
-2%281%29%5E3%2Ba%281%29%5E2%2Bb%2Bc=1
-2%2Ba%2Bb%2Bc=1
2.a%2Bb%2Bc=3
and
f%28-2%29=-2
-2%28-2%29%5E3%2Ba%28-2%29%5E2-2b%2Bc=-2
16%2B4a-2b%2Bc=-2
3.4a-2b%2Bc=-18
.
.
.
Subtract 2 from 1,
4a%2B2b%2Bc-a-b-c=16-3
4.3a%2Bb=13
Subtracting 2 from 3,
4a-2b%2Bc-a-b-c=-18-2
3a-3b=-21
5.a-b=-7
Adding 4 and 5,
3a%2Bb%2Ba-b=13-7
4a=6
a=3%2F2
Then,
3%283%2F2%29%2Bb=13
9%2F2%2Bb=26%2F2
b=17%2F2
And,
3%2F2%2B17%2F2%2Bc=3
10%2Bc=3
c=3-10
c=-7
So,
f%28x%29=-2x%5E3%2B%283%2F2%29x%5E2%2B%2817%2F2%29x-7
and
f%28-1%29=-2%28-1%29%5E3%2B%283%2F2%29-%2817%2F2%29-7
f%28-1%29=-12

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y - axis at 2. If f(1) = 1, and f(-2)= -2, find f(-1) and write the complete function.
Complete function: highlight_green%28f%28x%29+=+-+2x%5E3+-+3x%5E2+%2B+4x+%2B+2%29

f%28-+1%29+=+-+2%28-+1%29%5E3+-+3%28-+1%29%5E2+%2B+4%28-+1%29+%2B+2

f%28-+1%29+=+-+2%28-+1%29+-+3%281%29+-+4+%2B+2

f%28-+1%29+=+2+-+3+-+4+%2B+2 =========> highlight_green%28f%28-+1%29+=+-+3%29