Answer the question.
-Determine the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ so that its graph contains the points $( - 1 , - 9 ) , ( 0 , - 3 ) , ( 1,7 )$, and $( 2,33 )$.
A) $f ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$
B) $f ( x ) = 3 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$
C) $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + 6 x + 3$
D) $f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 6 x + 3$

Question

Quizplus · Accepted Answer

To determine the correct function, we substitute each point into the general form $f(x) = ax^3 + bx^2 + cx + d$ and solve for $a$, $b$, $c$, and $d$. For option A, substituting the points into $f(x) = 2x^3 + 2x^2 + 6x - 3$ yields:1. For $(-1, -9)$: $2(-1)^3 + 2(-1)^2 + 6(-1) - 3 = -2 + 2 - 6 - 3 = -9$2. For $(0, -3)$: $2(0)^3 + 2(0)^2 + 6(0) - 3 = -3$3. For $(1, 7)$: $2(1)^3 + 2(1)^2 + 6(1) - 3 = 2 + 2 + 6 - 3 = 7$4. For $(2, 33)$: $2(2)^3 + 2(2)^2 + 6(2) - 3 = 16 + 8 + 12 - 3 = 33$Each point satisfies the equation for option A, confirming it as the correct function.

Answer the Question f(x)=ax3+bx2+cx+df ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + df(x)=ax3+bx2+cx+d

Answer the Question $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$