22 f x = - 6x^2 + 60x - 126 ^ h The function f is defined by the given equation. Which of the following equivalent forms of the equation displays the maximum value of the function as a constant or coefficient?
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice C is correct. The given equation is quadratic. The maximum value of a function defined by a quadratic equation can be displayed as a constant in the = - 2+ vertex form of the equation, f^xh a^x hh k, where the maximum value of the = function is k, which occurs when x h, and a is a constant. The given equation can be rewritten in this form by completing the square. To complete the square, =-6 2-10 -126 the given equation can be rewritten as f^xh ^x xh , which is =-6 2-10 +25 -126+6 25 =-6 -5 2+24 equivalent to f^xh ^x x h ^ h, or f^xh ^x h . This =- = =24 equation is in vertex form, where a 6, h 5, and k . Therefore, =-6 -5 2+24 24 f^xh ^x h displays the maximum value, , of the function as a constant. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. This form displays one of the zeros, not the maximum value, of the function as a constant. Choice D is incorrect. This form displays the zeros, not the maximum value, of the function as constants.
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