Which set of parametric equations represents the graph of the following rectangular equation using $t = 6 - x$ ?
$y = x ^ { 2 } + 2$
A)
$x = t + 6$
$y = ( t + 6 ) ^ { 2 } - 2$
B)
$x = t - 6$
$y = ( t - 6 ) ^ { 2 } - 2$
C)
$\begin{array} { l }
x = t - 6 \
y = ( t - 6 ) ^ { 2 } + 2
\end{array}$
D)
$x = 6 + t$
$y = ( 6 + t ) ^ { 2 } + 2$
E)
$\begin{array} { l }
x = 6 - t \
y = ( 6 - t ) ^ { 2 } + 2
\end{array}$

Question

Which set of parametric equations represents the graph of the following rectangular equation using $t = 6 - x$ ?
$y = x ^ { 2 } + 2$
A)
$x = t + 6$
$y = ( t + 6 ) ^ { 2 } - 2$
B)
$x = t - 6$
$y = ( t - 6 ) ^ { 2 } - 2$
C)
$\begin{array} { l } 
x = t - 6 \
y = ( t - 6 ) ^ { 2 } + 2
\end{array}$
D)
$x = 6 + t$
$y = ( 6 + t ) ^ { 2 } + 2$
E)
$\begin{array} { l } 
x = 6 - t \
y = ( 6 - t ) ^ { 2 } + 2
\end{array}$

Quizplus · Accepted Answer

Given $t = 6 - x$, solving for $x$ gives $x = 6 - t$. Substituting $x = 6 - t$ into $y = x^2 + 2$ gives $y = (6 - t)^2 + 2$, which matches option E.

Which Set of Parametric Equations Represents the Graph of the Following