Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t + 2$ $y = t ^ { 2 }$
A) $y = t - 2$
B) $y = x ^ { 2 } + 4 x + 4$
C) $y = x ^ { 2 }$
D) $y = x ^ { 2 } - 4 x + 4$
E) $y = t + 2$

Question

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.  $x = t + 2$ $y = t ^ { 2 }$ 
A) $y = t - 2$
B) $y = x ^ { 2 } + 4 x + 4$
C) $y = x ^ { 2 }$
D) $y = x ^ { 2 } - 4 x + 4$
E) $y = t + 2$

Quizplus · Accepted Answer

To eliminate the parameter $t$, solve the first equation for $t$: $t = x - 2$. Substitute $t = x - 2$ into the second equation to get $y = (x - 2)^2$. Expanding this gives $y = x^2 - 4x + 4$, which matches option D.

Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose x=t+2x = t + 2x=t+2

Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose $x = t + 2$