Question

Graph each pair of parametric equations.

x=2t-1
y=t^2+5, -4 less than or equal to t less than or equal to 4

Answer 1

x=2t-1
\[y=t ^{2}+5, -4 \le t \le 4\]

Answer 2

use substitution to get a function in terms of x

\[t = \frac{x+1}{2}\]
\[y = \frac{(x+1)^2}{4} +5\]
this is a parabola with vertex at (-1,5)
change the limits ---> -9< x < 7
graph: