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Question

Investigate the given two parameter family of functions. Assume that a and b are positive. (a) Graph f(x) using b = 1 and three different values for a. (b) Graph f(x) using a = 1 and three different values for b. (c) In the graphs in parts (a) and (b), how do the critical points of f appear to move as a increases? As b increases? (d) Find a formula for the x-coordinates of the critical point(s) of f in terms of a and b. $f ( x ) = ( x - a ) ^ { 2 } + b$

Solution

VerifiedStep 1

1 of 5(a)

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