How do you convert parametric equation to cartesian x = t - 2 and y = -(t²) + t + 1?

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Answer 1 · 2016-09-08T08:56:56

#y= - x^2 - 3x -1#

separate out the #t# term

#x = t - 2 implies t = x + 2#

sub that into the other equation

#y = - t^2 + t + 1 #

#= - (x + 2)^2 + (x+2) + 1#

#= - (x^2 + 4x + 4) + x+3#

#implies y= - x^2 - 3x -1#