https://r2.erweima.ai/mathbot/image/1725878052404wrhmu7dx.jpg

The exercise is about Yves, a manager planning to reorganize the surface of his establishment to create a dance floor. The surface area of the dance floor is modeled by the quadratic function:

\[
f(x) = 2x^2 - 40x + 150
\]

This models the surface area of the dance floor in the interval \([0; 5]\), and Yves desires a dance floor of 50 m². The questions are related to this function.

### Question Breakdown:

1. **Complete the table of values**:
   - You are asked to calculate \(f(x)\) for the provided \(x\) values. Some are already filled out. For the remaining values, plug them into the given quadratic function.

2. **Graph the function**:
   - This involves visualizing the graph of \(f(x)\) by plotting it based on the values you found in the table. You will use a calculator's graphing mode.

3. **Solve \(f(x) = 0\)**:
   - You need to find the roots of the equation \(2x^2 - 40x + 150 = 0\). This can be done using either a calculator or the quadratic formula.

4. **Answer the final problem**:
   - Based on the results from the previous steps, provide a written conclusion about the situation (e.g., when the surface of the dance floor reaches the desired 50 m²).

---

Let me know if you'd like help with any of the calculations or further clarifications on any question. Would you like to go through solving the equation \(f(x) = 0\) next, or should we start by completing the table of values?

Yves est le gérant d’une brasserie. Il prévoit de réorganiser la surface de son établissement de manière à installer une piste de danse. La fonction f définie par f(x) = 2x² - 40x + 150 modélise la surface de la piste de danse sur l’intervalle [0 ; 5]. Yves souhaite une piste de danse de 50 m².

Explore how to solve a quadratic function to find the optimal surface area for a dance floor. This problem uses the equation f(x) = 2x² - 40x + 150, modeling the surface area within the interval [0; 5]. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation