Let a h and k be arbitrary real numbers with a 0 and let f be the function f x a x h k What familiar type of function is f

Question

Let a h and k be arbitrary real numbers with a 0 and let f be the function f x a x h k What familiar type of function is f Select an answer What information do you know about fjust by looking at its form There is no information that be gained simply by looking at the function f x in this form Parabola opens up if a 0 and opens down if a 0 Oh and k are the input and output of the parabola s vertex Next we use some calculus to develop familiar ideas from a different perspective To start treat a h and k as constants and compute f x f x Find all critical numbers of f These will depend on at lest one of a h and k X Assume a 0 Construct a first derivative sign chart for f Interval s where is negative Interval s where is positive Based on the information you ve found above classify the critical values of fas maxima or minima The critical value s at x

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