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.