https://file.aiquickdraw.com/mathbot/file/172904420918213svjk4f.jpg

The given equation is:

\[
E = 0.0000016x^2 - 0.016x + 54 \quad \text{where} \quad 1,800 \leq x \leq 5,400
\]

Where:
- \( E \) represents fuel efficiency (miles per gallon),
- \( x \) represents the weight of the SUV in pounds.

The question asks for the weight of the **least fuel-efficient SUV**, which corresponds to the minimum value of \( E \). To find this, we need to determine the vertex of the quadratic equation. The vertex formula for a quadratic function \( ax^2 + bx + c \) is:

\[
x = -\frac{b}{2a}
\]

For the given quadratic equation:

\[
a = 0.0000016, \quad b = -0.016
\]

Substitute these into the vertex formula:

\[
x = -\frac{-0.016}{2(0.0000016)} = \frac{0.016}{0.0000032} = 5000
\]

So, the least fuel-efficient SUV has a weight of **5,000 lbs**.

### Next part:
- **Would you trust the model for weights greater than the answer?** Since the model gives a range \( 1,800 \leq x \leq 5,400 \), the model is designed for this range. Trusting the model beyond this might not be reliable, as the relationship could change beyond the provided limits.

- **The model is "not trustworthy"** for vehicle weights larger than 5,400 pounds because the quadratic function predicts **increasing** fuel economy, which defies practical understanding as heavier vehicles generally have lower fuel economy.

Let me know if you'd like more details or have any other questions.

### 5 Related Questions:
1. How do you determine the maximum or minimum point of a quadratic equation?
2. What is the significance of the vertex in real-world applications like fuel efficiency?
3. How do you determine if a quadratic model is trustworthy outside its given range?
4. What does it mean when fuel economy increases with weight in real life?
5. How could you adjust this model to reflect a more accurate prediction for heavier vehicles?

### Tip:
For real-world data like fuel efficiency, ensure the model's range matches realistic physical behaviors outside the mathematical solution.

The fuel efficiency (in miles per gallon) of an SUV depends on its weight according to the formula E = 0.0000016x^2 - 0.016x + 54, where x is the weight of an SUV in pounds. According to the model, what is the weight of the least fuel-efficient SUV?

Learn how to use a quadratic function to determine the weight of the least fuel-efficient SUV based on the fuel efficiency formula E = 0.0000016x^2 - 0.016x + 54. This problem covers quadratic optimization and calculating the vertex of a parabola. Suitable for Grades 10-12.

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