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season 3 euphoria - Decision Point

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Question: An ornithologist tracks a bird’s migration pattern using GPS and finds that the bird flies along a path modeled by the equation $ y = 3x^2 - 12x + 15 $. What is the minimum altitude the bird reaches during its flight?

📌 Solution: The altitude is modeled by the quadratic function $ y = 3x^2 - 12x + 15 $. Since the coefficient of $ x^2 $ is positive, the parabola opens upward, and the minimum value occurs at the vertex. The x-coordinate of the vertex is:

📌 x = \frac{-(-12)}{2(3)} = \frac{12}{6} = 2

📌 Substitute $ x = 2 $ into the equation to find the minimum altitude:

📌 y = 3(2)^2 - 12(2) + 15 = 12 - 24 + 15 = 3

📌 Thus, the minimum altitude the bird reaches is $ \boxed{3} $.

📌 Question: A digital transformation firm offers two pricing plans: Plan A costs \$100 monthly plus \$10 per employee, and Plan B costs \$150 monthly plus \$7 per employee. For how many employees will the total monthly cost be the same under both plans?

📌 Solution: Let $ e $ represent the number of employees. The total cost for Plan A is $ 100 + 10e $, and for Plan B it is $ 150 + 7e $. Setting these equal:

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