Given the updated regression equation:

$y_1 = ax_1^2 + bx_1 + c$

with the parameters:

• $a = -2.31151$
• $b = 3.1369$
• $c = 9.53571$

We need to find the value of $y_1$ when $x_1 = 5$.

Substitute $x_1 = 5$ into the equation:

$y_1 = -2.31151(5)^2 + 3.1369(5) + 9.53571$

Let's calculate that.The value of $y_1$ when $x_1 = 5$ is approximately -32.57.

Would you like any further details on this calculation or have any other questions?

Here are some related questions you might consider:

1. What would be the value of $y_1$ if $x_1$ were 10 with this model?
2. How does the negative coefficient $a = -2.31151$ influence the shape of the graph?
3. What is the significance of the $R^2$ value in this context?
4. How would the value of $y_1$ change if the parameter $b$ was increased?
5. What does the constant $c = 9.53571$ represent in the context of this model?

Tip: A negative coefficient for $x^2$ indicates a downward-opening parabola, which is why $y_1$ decreases significantly as $x_1$ increases.