Question

Write a quadratic variation equation if g(x) varies directly with x2, and g(x) = 108 when x = 6.

If possible, please explain so I can learn.

Answer 1

This is direct variation; this means that if x increases, so does y.

The key is to translate that problem into appropriate formulas.

The general form of the equation for "quadratic variation" is y=k*x^2, where k is just a constant and is called the "constant of proportionality."

Here, we'll call this function g(x) = k*x^2.

We are told that g(6) = 108. Substitute 108 for g(x) in the above general equation and substitute 6 for x. Then solve the resulting equation for k.