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Question: A hydrologist is minimizing the energy cost of pumping water through an aquifer modeled by the function $f(x) = 2x^2 - 8x + 11$. Find the minimum value of $f(x)$.
This is a quadratic function in the form $f(x) = ax^2 + bx + c$, with $a = 2 > 0$, so the parabola opens upward and has a minimum at the vertex.
The x-coordinate of the vertex

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