# Sketching y^2 = X^3

## Homework Statement

Hi everyone, I am not sure how to sketch this:
y^2 = X^3
I have a feeling it will form a parabola.

If I find the square root of both sides I get:
y = X^3/2
Differentiating gives me

## The Attempt at a Solution

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Mentallic
Homework Helper
Think about the shape of the graph for y=x2, then y=x3, y=x4 etc. only for values x>0. The shape is roughly the same, no? The only difference is that for x>1 the graph is steeper and for 0<x<1 the graph is lower for larger powers.
So y=x3/2 will be roughly the same as y=x2 for x>0
But remember that when you take the square root of both sides, you need to remember that $$\pm$$ so your final result of $$y^2=x^3$$ or $$y=\pm x^{3/2}$$ is the graph of y=x3/2 for values of x>0 and then exactly the same thing but reflected in the x-axis for y=-x3/2.

Mark44
Mentor

## Homework Statement

Hi everyone, I am not sure how to sketch this:
y^2 = X^3
I have a feeling it will form a parabola.

If I find the square root of both sides I get:
y = X^3/2
Actually, it's
$$y = \pm x^{3/2}$$
There are two branches.
Differentiating gives me
The derivative also has two branches.
$$dy/dx = \pm 1.5x^{1/2}$$