Find a rectangular equation for the parametric equation x=t^2 y=2t+3 for t in[-3,3]

Solve the second equation for t, then substitute into the first.
.. y = 2t +3
.. y -3 = 2t
.. (y -3)/2 = t

.. x = t^2
.. x = ((y -3)/2)^2
.. x = (1/4)(y -3)^2 . . . . . . your rectangular equation, good for y in [-3, 3]

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