
Using your calculator to do a quadratic regression, express the profit as a function of the number of items sold.
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*Round all numbers to 1 decimal place.*

To express the profit \( P(x) \) as a function of the number of items sold \( x \) using quadratic regression, you need to follow these general steps:

1. **Collect Data**: You would normally have a set of data points that give you the number of items sold \( x \) and the corresponding profit \( P(x) \).
2. **Enter Data into the Calculator**: Use your calculator's quadratic regression feature by entering the \( x \) values (number of items sold) and \( P(x) \) values (profit for each quantity).
3. **Perform Quadratic Regression**: The calculator will output a quadratic equation of the form:

\[
P(x) = ax^2 + bx + c
\]

where \( a \), \( b \), and \( c \) are constants determined by the regression.

4. **Round Values**: After the regression, round \( a \), \( b \), and \( c \) to 1 decimal place to form the final quadratic function for profit.

### Example:
Assume you have performed the regression, and the calculator gives you the following equation:
\[
P(x) = 2.3x^2 - 5.1x + 12.7
\]

Here, \( a = 2.3 \), \( b = -5.1 \), and \( c = 12.7 \) have all been rounded to one decimal place.

Would you like help with specific data points to perform this regression, or are you looking for clarification on any step?

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**Relative questions:**
1. How do you enter data into the calculator for a quadratic regression?
2. What are typical use cases for quadratic regression in business contexts?
3. How do you interpret the coefficients \( a \), \( b \), and \( c \) in a profit function?
4. What does it mean when \( a \) is positive or negative in a quadratic equation?
5. Can a quadratic regression model be applied to any type of data?

**Tip**: When using quadratic regression, always double-check your data input for accuracy to ensure precise results.

Using your calculator to do a quadratic regression, express the profit as a function of the number of items sold. *Round all numbers to 1 decimal place.*

Learn how to use quadratic regression to express the profit as a function of the number of items sold. This example demonstrates how to round the coefficients to 1 decimal place and interpret the equation P(x) = ax^2 + bx + c. Suitable for students in Grades 9-12.

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