The function g is defined by g(x) = (x + 14)(t − x), where t is a constant. In the xy-plane, the graph of y = g(x) passes through the point (24, 0). What is the value of g(0) ?

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The correct answer is 336. By the zero product property, if (x + 14)(t − x) = 0, then x + 14 = 0, which gives x = −14, or t − x = 0, which gives x = t. Therefore, g(x) = 0 when x = −14 and when x = t. Since the graph of y = g(x) passes through the point (24, 0), it follows that g(24) = 0, so t = 24. Substituting 24 for t in the equation g(x) = (x + 14)(t − x) yields g(x) = (x + 14)(24 − x). The value of g(0) can be calculated by substituting 0 for x in this equation, which yields g(0) = (0 + 14)(24 − 0), or g(0) = 336.

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