To address the equation provided:

$y = \sqrt[3]{x^2}$

with the conditions $y = 0$ and $x = 1$.

1. First, let's analyze the condition $y = 0$:

Given $y = \sqrt[3]{x^2}$,

$0 = \sqrt[3]{x^2}$

This implies that $x^2 = 0$, hence $x = 0$.

So, when $y = 0$, $x$ must be 0.

2. Now, let's analyze the condition $x = 1$:

Given $x = 1$,

[ y = \sqrt[3]{1^2} = \sqrt[3]{1} = 1 ]

So, when $x = 1$, $y = 1$.

Therefore, the conditions show the following points:

• When $y = 0$, $x = 0$
• When $x = 1$, $y = 1$

Do you have any questions or would you like further details on this problem? Here are some additional questions you might consider:

1. How can you find the derivative of $y = \sqrt[3]{x^2}$?
2. What is the behavior of the function $y = \sqrt[3]{x^2}$ as $x$ approaches infinity?
3. How do you plot the graph of $y = \sqrt[3]{x^2}$?
4. What are the critical points of the function $y = \sqrt[3]{x^2}$?
5. How does the function $y = \sqrt[3]{x^2}$ compare to $y = x^2$?

Tip: When solving equations involving roots and powers, always check for potential extraneous solutions and ensure the domain is properly considered.