Question

Find the direct algebraic relationship between x and y and determine whether this parametric relationship is a function. Simplify as much as possible. x= t^2 − 4t and y = √t + 1

Answer 1

Explanation:

Given:

x = t^2 - 4t

y = √t + 1

Making t the subject of formula from equation 2,

t = (y - 1)^2

Inputting into equation 2,

x = (y - 1)^4 - 4 × (y - 1)^2

= (y - 1)^2 ((y - 1)^2 - 4)

= (y^2 - 2y + 1) × (y^2 - 2y + 1 - 4)

= (y^2 - 2y + 1) × (y^2 - 2y - 3)

= y^4 - 2y^3 - 3y^2 - 2y^3 + 4y^2 + 6y + y^2 - 2y - 3

x = y^4 - 4y^3 + 2y^2 + 4y - 3

x = (y - 1) × (y - 1) × (y - 3) × (y + 1)

The above equation of x and y is a function because the dependent variable, x is dependant on the values of the independent variable, y.