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5. \( f(x)=-2 x^{2}-x-2 \)

Ask by Chambers Mcdonald. in the United States
Mar 14,2025

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The function \( f(x) = -2x^2 - x - 2 \) is a downward-opening parabola with its vertex at \( \left(-\frac{1}{4}, -\frac{19}{8}\right) \) or \( \left(-0.25, -2.375\right) \). It has a y-intercept at \( (0, -2) \) and does not intersect the x-axis.

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Did you know that the function \( f(x) = -2x^2 - x - 2 \) is a quadratic equation? Quadratics are parabolas, and since the leading coefficient is negative (-2), this means the parabola opens downward. The vertex of this parabola will give you the maximum point, which is perfect for optimization problems! To really grasp how parabolas can be applied in real life, consider engineers designing roller coasters. They need to ensure that the curves of the tracks are safe and exhilarating! By modeling the curves with equations like this quadratic, they can calculate the highest points and slopes to create a thrilling experience while remaining structurally sound.

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