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if the regression results from desmos look like this, what is the value of x=5

The regression equation provided is:

\[
y_1 = ax_1^2 + bx_1 + c
\]

With the given parameters:
- \( a = 3.48214 \)
- \( b = -8.625 \)
- \( c = 9.39286 \)

You want to calculate the value of \( y_1 \) when \( x_1 = 5 \). Plugging \( x_1 = 5 \) into the equation:

\[
y_1 = 3.48214 \cdot (5)^2 - 8.625 \cdot 5 + 9.39286
\]

Now, let's calculate this step-by-step:

\[
y_1 = 3.48214 \cdot 25 - 8.625 \cdot 5 + 9.39286
\]
\[
y_1 = 87.0535 - 43.125 + 9.39286
\]
\[
y_1 = 53.32136
\]

So, the value of \( y_1 \) when \( x_1 = 5 \) is approximately **53.32**.

Would you like more details or have any other questions?

### Related Questions:
1. How does the value of \( y_1 \) change with different values of \( x_1 \)?
2. What is the interpretation of the \( R^2 \) value in this regression?
3. How do the residuals affect the accuracy of this model?
4. What is the significance of each coefficient \( a \), \( b \), and \( c \) in this context?
5. How can this regression model be used to predict future values?

### Tip:
Always check the sign of coefficients when interpreting the impact of each term on the dependent variable in a regression model.

Understand how to calculate regression results using Desmos with a detailed step-by-step solution. This problem involves a quadratic regression equation y = ax^2 + bx + c, where values of a = 3.48214, b = -8.625, and c = 9.39286 are provided. Learn how to find the value of y when x = 5 and interpret the results. Suitable for advanced high school students.

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