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9) \( f(x)=x^{2}-2 \)

Ask by Clarke Hart. in Guatemala
Mar 10,2025

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La función \( f(x) = x^{2} - 2 \) es una parábola que se abre hacia arriba con vértice en \((0, -2)\). Su dominio es todos los números reales. Interseca el eje \(y\) en \((0, -2)\) y el eje \(x\) en \((\sqrt{2}, 0)\) y \((-\sqrt{2}, 0)\). El rango es \([-2, \infty)\).

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The Deep Dive

Did you know that the function \( f(x) = x^2 - 2 \) represents a parabola that opens upwards? Its vertex, which is the lowest point, is located at the coordinates (0, -2). This means that the function will take values greater than or equal to -2 for all real numbers x. The axis of symmetry is the y-axis, making it super easy to see how it behaves on either side of the vertex. In the real world, this function could model various scenarios, such as the trajectory of an object thrown upwards or the shape of a satellite dish. When you plot this function, the resulting graph resembles a U-shape, which is quite the popular design in nature, architecture, and engineering—all thanks to that charming quadratic form!

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