1. ## cunning curve sketching?

Hi everyone,

I was asked to sketch the curve $y = x(x - 5)^2$ which is shown in the attachment. The question then asks me to sketch the curve $y^2 = x(x - 5)^2$

My question to the forum is whether I can use the information from the first part of the question to derive the second sketch.

In these questions we cannot use graphing calculators and the idea is to sketch, not plot. Such questions are, quite frankly, tedious but I am thinking there is some kind of transformation that will make short work of it. Perhaps there isn't, I'm just asking the experts!

best wishes

2. ## Re: cunning curve sketching?

Note that the second curve is not a function. What you are actually sketching is two functions:

$y = (x-5)\sqrt{x}$

and

$y = -(x-5)\sqrt{x}$

Note that each function has a natural domain of $x\ge 0$. The two functions meet in two places, when $x=0$ and when $x=5$. They are mirror images of each other. So, sketch one and the other is just its mirror image across the $x$-axis.

Many thanks!