1. ## Transformation & Expression

It's quite embarrassing, but I can't remember how to "Find the dilation from the x-axis which takes y = x2 to the parabola with its vertex at the origin and which passes through the point (25, 15)".

Also, I'm struggling to "express the total surface area, S, of a cube as a function of the volume V of the cube".
From the previous part of this question, I had to find S "as a function of the length x of an edge", which was 6x2. I also know that V = x3.

Thanks.

2. ## Re: Transformation & Expression

Originally Posted by Fratricide
It's quite embarrassing, but I can't remember how to "Find the dilation from the x-axis which takes y = x2 to the parabola with its vertex at the origin and which passes through the point (25, 15)".

Also, I'm struggling to "express the total surface area, S, of a cube as a function of the volume V of the cube".
From the previous part of this question, I had to find S "as a function of the length x of an edge", which was 6x2. I also know that V = x3.

Thanks.
From what I read about dilation of the x-axis we want to find $y=(ax)^2$ such that $25=(15a)^2$

$25=(15a)^2$

$25=225a^2$

$\dfrac{25}{225}=a^2$

$\dfrac{1}{9}=a^2$

$a=\pm \dfrac{1}{3}$

b)
$A = 6s^2$

$V=s^3$

$s=\sqrt[3]{V}$

$A=6V^{2/3}$