Use a system of equations to find the cubic function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ that satisfies given equations. Solve the system using matrices.
$\begin{aligned}
f ( 2 ) & = - 26 \
f ( - 2 ) & = 6 \
f ( 1 ) & = 0 \
f ( - 1 ) & = - 2
\end{aligned}$
A) $a = 2 , b = - 2 , c = 1 , d = - 1$
B) $a = - 26 , b = 6 , c = 0 , d = - 2$
C) $a = - 3 , b = - 3 , c = 4 , d = 2$
D) $a = - 26 , b = 30 , c = - 12 , d = 16$
E) $a = 50,598 , b = - 54,650 c = - 730 , d = 518$

Question

Quizplus · Accepted Answer

Substituting the given values of $x$ into the cubic function $f(x) = ax^3 + bx^2 + cx + d$ yields a system of linear equations. Solving this system using matrices or any other method reveals that the coefficients that satisfy all given conditions are $a = -3$, $b = -3$, $c = 4$, and $d = 2$.

Use a System of Equations to Find the Cubic Function f(x)=ax3+bx2+cx+df ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + df(x)=ax3+bx2+cx+d

Use a System of Equations to Find the Cubic Function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$