Find the cubic or quartic function that models the data in the table.
-$\begin{array}{c|cccc}
x & -3 & 1 & 3 & 4 \
\hline y & 50 & -3 & -45 & -102
\end{array} \text { (Cubic) }$

A) $y = - 1.83 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$
B) $y = - 1.53 x ^ { 3 } + 0.54 x ^ { 2 } - 2.07 x + 0.36$
C) $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$
D) $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.57 x + 0.36$

Question

Find the cubic or quartic function that models the data in the table.
-$\begin{array}{c|cccc}
x & -3 & 1 & 3 & 4 \
\hline y & 50 & -3 & -45 & -102
\end{array} \text { (Cubic) }$

A) $y = - 1.83 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$
B) $y = - 1.53 x ^ { 3 } + 0.54 x ^ { 2 } - 2.07 x + 0.36$
C) $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$
D) $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.57 x + 0.36$

Quizplus · Accepted Answer

Given the data points, the correct cubic function that models the data is $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$. This can be determined by either using a system of equations to solve for the coefficients of a cubic function $ax^3 + bx^2 + cx + d$ given the x and y values from the table, or by using a graphing tool or software that fits a cubic model to the data points. The coefficients closely match those in option C, making it the correct choice.

Find the Cubic or Quartic Function That Models the Data x−3134y50−3−45−102 (Cubic) \begin{array}{c|cccc}x & -3 & 1 & 3 & 4 \\\hline y & 50 & -3 & -45 & -102\end{array} \text { (Cubic) }xy​−350​1−3​3−45​4−102​​ (Cubic)

Find the Cubic or Quartic Function That Models the Data $\begin{array}{c|cccc}x & -3 & 1 & 3 & 4 \\\hline y & 50 & -3 & -45 & -102\end{array} \text { (Cubic) }$