math-functions

If y = x^2 + 5x - 9,for what values of x is y>5?

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  1. To find range of x for which f(x)>5, where
    f(x) = x^2 + 5x - 9
    Solve for y=5, or
    5 = x^2 + 5x - 9
    x^2 + 5x - 14 = 0
    (x-2)(x+7)=0

    Since f(x) is U-shaped, the part of f(x) for -7<x<2 is below the line y=5.
    So the part of f(x) above the horizontal line y=5, or f(x)>5 is (-∞-7)∪(2,∞).

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