First, if y varies as the square of x, that means:
y = kx2
where k is the constant of proportionality. When thinking about change, I like to use subscripts to represent before and after. We will use a subscript of 1 to denote before (or the initial value of a variable) and a subscript of 2 to represent after (or the final value of a variable). So, y1 is the initial and y2 is the final. Also, x1 is the initial and x2 is the final. k does not change, so it doesn't get any subscripts. Thus, we can write two equations, because the above equation must hold before and after.
y1 = k(x1)2
y2 = k(x2)2
This is not obvious, but after a few times it becomes natural. We can now eliminate k. An easy way to do that is to divide the second equation by the first to get:
y2 / y1 = (x2)2 / (x1)2
The right hand side of the equation can be written in another form, to get:
y2 / y1 = ( x2 / x1 )2
Okay... so why did I do this? Because we are talking about factors of change, not absolute changes. So, y2/y1 represents the factor change of y and x2/x1 represents the factor change of x. Thus, when the prompt says x is doubled, we can understand that to mean that:
x2/x1 = 2
And we can determine the factor change of y by substituting 2 for the the factor change of x.
y2 / y1 = (2)2 = 4
So, when x is doubled, y is quadrupled. quadrupled when x is doubled.
Step-by-step explanation:
Hope it helps
Brainlest me
#Carry on learning
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