Eliminate the parameter. x = t - 3, y = t2 + 5

y = x^2 + 6x+14

Step-by-step explanation:

x = t - 3, y = t^2 + 5

x=t-3

Add 3 to each side

x+3 = t-3+3

x+3 = t

Substitute into the second equation

y = t^2 + 5

y = (x+3) ^2 + 5

Foil the first term

y = (x+3) (x+3) + 5

y = (x^2 + 3x+3x+9) + 5

y = x^2 + 6x+9) + 5

y = x^2 + 6x+14