Question

Consider the parametric equations below.

x = t^2 − 3, y = t + 2, −3 ≤ t ≤ 3
Eliminate the parameter to find a Cartesian equation of the curve.
for
−1 ≤ y ≤ 5

Answer 1

Solve the second equation for
`t`, then substitute it into the first equation.

`y = t + 2 \implies t = y-2`

`x = t^2 - 3 \implies \boxed{x = (y-2)^2 - 3}`