Question

Variable y varies directly with x2, and y = 96 when x = 4.

What is the value of y when x = 2?

y =_________

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Variable y varies directly with x2, and y = 180 when x = 6.

Enter the constant of variation in the quadratic variation equation?


y = ________x2

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Answer 1

Direct variation is y = kx, where k is the constant of variation.
But now it says y varies directly with x2 (or 2x), so now the x in the equation is 2x.

The equation is y = k(2x)
Now you find k.
y = 96 when x = 4.
(96) = k(2*4)
96 = k(8)
k = 12

The equation is now y = 12(2x)
To find the value of y when x=2, plug 2 into the equation you made. y = 12(2*2) y = 48
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Now it's with a "quadratic variation," which is the same thing except x is squared.
The equation is y = kx^2

But y varies directly with x2 (same thing as 2x), so now it's y = k(2x)^2.

Now you find k by substituting y and x values that were given.
y = 180 when x = 6
(180) = k(2*6)^2
180 = k(12)^2
180 = k(144)
k = 1.25
k, 1.25, is the constant of variation.