The problem states that $y$ is directly proportional to $x^2$. This means the relationship between $y$ and $x$ can be described by the equation:

$y = kx^2$

where $k$ is the constant of proportionality.

Steps to find the constant $k$:

1. Pick a point on the graph where both $x$ and $y$ values are easy to read. Looking at the graph, a point such as $(x, y) = (2, 4)$ seems appropriate.

2. Substitute the values of $x$ and $y$ into the equation: $4 = k \cdot 2^2$ Simplifying this: $4 = k \cdot 4$ Dividing both sides by 4: $k = 1$

Thus, the constant of proportionality is $k = 1$, and the equation becomes: $y = x^2$

Would you like further details on this solution?

Here are five related questions for practice:

1. What happens to $y$ if $x$ is doubled in this relationship?
2. Can you find the value of $y$ when $x = -3$?
3. How would the graph change if the constant of proportionality $k$ were greater than 1?
4. What is the significance of direct proportionality in other real-world problems?
5. How would the equation change if $y$ were inversely proportional to $x^2$?

Tip: Always pick a point where both the $x$- and $y$-values are easily readable to avoid calculation errors!