The points given are \((1,1)\), \((2,4)\), \((3,9)\), and \((4,16)\). You want to find the value of \(y\) when \(x = 2.5\).

These points suggest that the relationship between \(x\) and \(y\) is quadratic because the \(y\) values are squares of the \(x\) values:

\[
y = x^2
\]

For \(x = 2.5\):

\[
y = (2.5)^2 = 6.25
\]

So, when \(x = 2.5\), \(y = 6.25\).

Would you like more details or have any questions? 

Here are some related questions you might find useful:
1. How do you determine the equation of a quadratic function given a set of points?
2. What are other methods to interpolate values between given points?
3. How can you generalize this approach for other types of functions?
4. What is the significance of recognizing patterns in a set of points?
5. How do you calculate the square of a decimal value accurately?

**Tip:** When identifying patterns in sequences, it's often helpful to look for consistent differences or ratios between terms to deduce the underlying function.

Explore the relationship between x and y in quadratic equations with this problem. Discover how to find y when x = 2.5 using the quadratic formula y = x^2. Suitable for students studying quadratic equations.

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