Question

Eliminate the parameter. x = square root of t, y = 4t + 1

Answer 1

X = sqrt t 
t = x^2 

y = 4t + 1 
4t = y - 1
t = (y-1) / 4

equate the 2 values of t:_

x^2  = (y - 1) /  4

4x^2  = y - 1

y = 4x^2 + 1

Answer 2

$\sqrt{t}, y=4t+1$

change $x=\sqrt{t}$ into $x^{2} =t$ to get rid of the square root. Keep in mind that if you need to graph the equation, x>=0 because there can't be a negative under the square root.

Then substitute $x^{2}$ into y=4t+1 for t and you get:
$y=4 x^{2} +1$