Help me math problem about direct proportional (5*)?

y ∝ x²
Then y = k x²
where k is a non-zero constant.

The difference in the values of y when x = 1 and x = 3 is 32 :
k (3)² - k (1)² = 32
8k = 32
k = 4
Then, y = 4 x²

When x = -2 :
y = 4 * (-2)²
y = 16

y ∝ x²

Hence, y = kx²

With x = 1, we have y = k and with x = 3 we have y = 9k

so, 9k - k = 32

i.e. 8k = 32

=> k = 4

Therefore, y = 4x²

so, when x = -2 we have:

y = 4(-2)² => 16

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