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Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.

1. The roots of the quadratic function describing the relationship between the number of products produced and the overall profit margin are [tex]\(x=0\)[/tex] and [tex]\(x=26\)[/tex].
2. The vertex of the function is [tex]\((13, -50)\)[/tex], which is a minimum point.
3. The company loses money on their first few products as it costs them more to make them, but once they produce [tex]\( \square \)[/tex] items, they break even again.
4. The worst-case scenario is that they produce [tex]\( \square \)[/tex] items, resulting in a profit of [tex]\(\square\)[/tex] dollars.
5. The first root indicates that the profit is zero when zero products are sold.



Answer :

GinnyAnswer
Given the roots and vertex of the quadratic function describing the relationship between the number of products produced and overall profit margin, we can answer the questions and interpret the key features:

1. Breaking Even Point:
- Break-even occurs when the profit is zero. This happens at the roots of the quadratic function.
- The first root [tex]\( x = 0 \)[/tex] indicates that the profit is zero when 0 products are sold.
- The second root [tex]\( x = 26 \)[/tex] indicates that the company breaks even again when they produce 26 items.

So, the company breaks even again when they hit 26 items.

2. Worst Case Scenario:
- The vertex of the quadratic function represents either the maximum or minimum point of the function. In this case, since the vertex [tex]\( (13, -50) \)[/tex] is a minimum, it represents the worst-case scenario.
- At the vertex, the company produces 13 items and has a profit of [tex]\(-50\)[/tex] dollars.

Therefore, in the worst case scenario, they produce 13 items, resulting in a profit of -50 dollars.

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