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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!

y is directly proportional to x^2. Using the graph below, work out the constant of proportionality.

Learn how to find the constant of proportionality for the equation y = kx^2 using a graph. This problem involves key mathematical concepts such as direct proportionality and quadratic relationships. Suitable for students in Grades 8-9.

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