Find the algebraic relationship between x and y:
x = 5 – 4t^2 and y = 2t - 2
Thank you!!
if y = 2 t - 2
then t = (y+2)/2
use that
x = 5 - 4 [ (y+2)/2)^2 ]
x = 5 - 4 [ (y^2 + 4 y + 4)/4]
x = 5 - y^2 - 4 y - 4
x = - y^2 - 4 y +1
-y^2 - 4 y = x-1
y^2 + 4 y = 1-x
To find the algebraic relationship between x and y, we can substitute the value of t from one equation into the other equation. Let's solve for t in the equation y = 2t - 2:
y = 2t - 2
Rearranging the equation, we get:
2t = y + 2
Dividing both sides by 2, we have:
t = (y + 2) / 2
Now that we have the value of t, we can substitute it into the equation x = 5 – 4t^2:
x = 5 – 4[(y + 2) / 2]^2
Simplifying further, we get:
x = 5 - 4(y + 2)^2 / 4
x = 5 - (y + 2)^2
So, the algebraic relationship between x and y is given by:
x = 5 - (y + 2)^2