Question

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.

Answer 1

y = -2 x^3 + b x^2 + c x + d
y(0) = 2 so d = 2

y = -2 x^3 + b x^2 + c x + 2

1 = -2 + b + c + 2 or b+c=1
-2 = 16 + 4 b - 2 c + 2 or -20 = 4 b - 2 c
or -10 = 2 b - c

2 b - 1 c = -10
1 b + 1 c = 1
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3 b = - 9
b = -3 etc

Answer 2

I need a cubic trinomial in standard form