if y is directly proportional to x2 and the difference in the values of y when x = 1 and x = 3 is 32, find the value of y when x = -2

Question

If y is directly proportional to x2 and the difference in the value of y when x = 1 and x = 3 is 32,find the value of y when x = -2

Answer 1

Given y is directly proportional to x², means there is a constant k so that y = k * x².

 

For x = 1 y(1) = k and for x =3 y(3) =9k

Now y(3) - y(1) = 9k - k = 8k = 32

k = 4

 

The relationship is y = 4x²

 

For x = -2, y = 4 * (-2)² = 16