Give me a word problem that is about graphs, something like y=mx+c or y=(x^2+a)+b just as long as it can be treated as a real world problem, please generate 3 examples

Here are three real-world word problems involving linear and quadratic graphs:

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### Problem 1: **Linear Equation - Cost of Car Rentals**
A car rental company charges a flat fee of $50 plus an additional $0.30 per mile driven. Let **y** represent the total cost of renting the car, and **x** represent the number of miles driven.

- **Question**: Write an equation that represents the cost of renting a car as a function of the miles driven. If a customer drives 150 miles, what will be the total cost?

*(Hint: The equation follows the form $ y = mx + c $, where $ m $ is the rate per mile and $ c $ is the flat fee.)*

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### Problem 2: **Quadratic Equation - Maximum Height of a Basketball Shot**
A basketball player shoots a ball, and its height **y** in feet after **x** seconds is given by the equation $ y = -16x^2 + 48x + 6 $, where the term $ -16x^2 $ accounts for gravity, $ 48x $ is the initial velocity, and 6 feet is the initial height.

- **Question**: How long will it take for the basketball to reach its maximum height? What is the maximum height reached by the ball?

*(Hint: The graph of a quadratic equation forms a parabola, and the maximum height occurs at the vertex of the parabola.)*

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### Problem 3: **Linear Equation - Temperature Conversion**
The temperature $ T $ in degrees Fahrenheit can be related to the temperature $ C $ in degrees Celsius by the equation $ T = 1.8C + 32 $.

- **Question**: If the temperature outside is 25°C, what is the temperature in Fahrenheit? What is the Fahrenheit temperature when it's freezing point (0°C)?

*(Hint: The equation follows the linear form $ T = mC + c $, where $ m $ is the conversion factor, and $ c $ is the constant that shifts the scale.)*

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Would you like a detailed explanation or solution for any of these problems? 

### 5 Related Questions:
1. How would the graph of a linear function change if the slope is increased?
2. What are the key points to find when graphing a quadratic equation like $ y = -16x^2 + 48x + 6 $?
3. How can you interpret the slope and intercept in real-world linear functions like the car rental problem?
4. What does the vertex of a quadratic equation represent in physical problems?
5. How would you solve for $ x $ if the cost of the car rental is $80?

### Tip:
In quadratic equations, the vertex formula $ x = \frac{-b}{2a} $ can quickly find the maximum or minimum value.

Explore three real-world math problems involving linear and quadratic equations, such as car rental costs, basketball shot heights, and temperature conversions. Learn how to model situations using y = mx + c and y = ax^2 + bx + c, and solve practical questions suitable for Grades 8-10.

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