Give two parametric representations for the equation of the parabola.
-$$y = ( x - 2 ) ^ { 2 } - 1$$
A) $x = t , y = ( t + 2 ) ^ { 2 } - 1$ for $t$ in $( \infty , \infty ) ; x = t + 2 , y = t ^ { 2 } - 1$ for $t$ in $( \infty , \infty )$
B) $x = t , y = ( t - 2 ) ^ { 2 } - 1$ for $t$ in $( \infty , \infty ) ; x = t + 2 , y = t ^ { 2 } - 1$ for $t$ in $( \infty , \infty )$
C) $x = t , y = ( t - 2 ) ^ { 2 } - 1$ for $t$ in $( \infty , \infty ) ; x = t - 2 , y = t ^ { 2 } - 1$ for $t$ in $( \infty , \infty )$
D) $x = t , y = ( t + 2 ) ^ { 2 } - 1$ for $t$ in $( \infty , \infty )$; $x = t - 2 , y = t ^ { 2 } - 1$ for $t$ in $( \infty , \infty )$

Question

Quizplus · Accepted Answer

Option B correctly represents the given parabola $y = (x - 2)^2 - 1$ in two parametric forms. The first part, $x = t, y = (t - 2)^2 - 1$, directly substitutes $x$ with $t$, maintaining the original equation's structure. The second part, $x = t + 2, y = t^2 - 1$, shifts $t$ to match the vertex form by making $x = t + 2$, simplifying the equation to $y = t^2 - 1$.

Give Two Parametric Representations for the Equation of the Parabola y=(x−2)2−1y = ( x - 2 ) ^ { 2 } - 1y=(x−2)2−1

Give Two Parametric Representations for the Equation of the Parabola $y = ( x - 2 ) ^ { 2 } - 1$