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why is 67 so popular - Coaching Toolbox

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Subtract 15 from both sides:

📌 k = \frac{33}{9} = \frac{11}{3}

📌 Thus, the value of $ k $ is $ \boxed{\frac{11}{3}} $.

📌 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:

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