Give two parametric representations for the equation of the parabola.
-$$y = x ^ { 2 } - 6 x + 13$$
A) $x = t , y = t ^ { 2 } - 6 t - 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 4$ for $t$ in $( \infty , \infty )$
B) $x = t , y = t ^ { 2 } + 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 4$ for $t$ in $( \infty , \infty )$
C) $x = t , y = t ^ { 2 } + 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 4$ for $t$ in $( \infty , \infty )$
D) $x = t , y = t ^ { 2 } - 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 4$ for $t$ in $( \infty , \infty )$

Question

Quizplus · Accepted Answer

The first representation in option D directly matches the given equation with $x = t$, and the second representation is a shifted version where $x = t - 3$ simplifies the equation to a form $y = t^2 + 4$, correctly representing the parabola.

Give Two Parametric Representations for the Equation of the Parabola y=x2−6x+13y = x ^ { 2 } - 6 x + 13y=x2−6x+13

Give Two Parametric Representations for the Equation of the Parabola $y = x ^ { 2 } - 6 x + 13$