Question

What is the rectangular form of the parametric equations?x(t)= t+3 ,y(t)=2t^2 −4, where t is on the interval [−3,1].

Answer 1

x= t + 3

Solve for t

t = x - 3

Substitute in the other equation:

y= 2 (x-3)^2 - 4

y= 2 ( x^2 - 6x + 9 ) - 4

y= 2x^2 -12x + 18 - 4

y= 2x^ - 12x + 14