Provide an appropriate response.
-If the points in the table lie on a parabola, write the equation whose graph is the parabola. $\begin{array}{c|c|c|c|c|c|c}
\mathrm{x} & 5 & 4 & 3 & 2 & 1 & 0 \
\hline \mathrm{y} & -24 & -9 & 0 & 3 & 0 & -9
\end{array}$

A) $y = - 3 x ^ { 2 } + 12 x - 9$
B) $y = - 3 ( x + 2 ) ^ { 2 } + 3$
C) $y = - 3 ( x + 2 ) ^ { 2 } - 3$
D) $y = 3 x ^ { 2 } + 12 x - 9$

Question

Provide an appropriate response.
-If the points in the table lie on a parabola, write the equation whose graph is the parabola. $\begin{array}{c|c|c|c|c|c|c}
\mathrm{x} & 5 & 4 & 3 & 2 & 1 & 0 \
\hline \mathrm{y} & -24 & -9 & 0 & 3 & 0 & -9
\end{array}$

A) $y = - 3 x ^ { 2 } + 12 x - 9$
B) $y = - 3 ( x + 2 ) ^ { 2 } + 3$
C) $y = - 3 ( x + 2 ) ^ { 2 } - 3$
D) $y = 3 x ^ { 2 } + 12 x - 9$

Quizplus · Accepted Answer

The correct equation is $y = - 3 x ^ { 2 } + 12 x - 9$. This can be determined by observing the symmetry of the y-values around the x-value of 2, suggesting a vertex form of a parabola. However, converting it to standard form $y = ax^2 + bx + c$ and using the given points to solve for $a$, $b$, and $c$, we find that $a = -3$, $b = 12$, and $c = -9$, which matches option A.

Provide an Appropriate Response x543210y−24−9030−9\begin{array}{c|c|c|c|c|c|c}\mathrm{x} & 5 & 4 & 3 & 2 & 1 & 0 \\\hline \mathrm{y} & -24 & -9 & 0 & 3 & 0 & -9\end{array}xy​5−24​4−9​30​23​10​0−9​​

Provide an Appropriate Response $\begin{array}{c|c|c|c|c|c|c}\mathrm{x} & 5 & 4 & 3 & 2 & 1 & 0 \\\hline \mathrm{y} & -24 & -9 & 0 & 3 & 0 & -9\end{array}$