Write a set of parametric equations for [tex]y = x^2 + 1[/tex] given the parameter [tex]t = x - 2[/tex].

t = x − 2 ⇒ x = t + 2 y = x 2 + 1 ⇒ y = ( t + 2 ) 2 + 1 = t 2 + 4 t + 5 { y = t 2 + 4 t + 5 x = t + 2 ​

Answered by kate200468 | 2024-06-10

The parametric equations for the function y = x 2 + 1 with the parameter t = x − 2 are x = t + 2 and y = t 2 + 4 t + 5 . This allows you to represent the same parabola using a parameter. By varying t , you can find different points on the curve easily.
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Answered by kate200468 | 2024-11-12