Question 1106859
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The calculus approach used by one of the other tutors is fine.  But not if you don't know calculus.<br>
The solution by the other tutor is correct; but without explanation it might not be of much help.<br>
The given function graphs as a parabola, because it (in its expanded form) has an x^2 term.  In the given function 1-(x-6)^2, the value of the expression in parentheses is always 0 or positive.  So in evaluating the function for a particular value of x, you will be subtracting 0 or a positive number from 1.<br>
That means the maximum value of the function is 1.  And that maximum value occurs when (x-6)^2 is 0, which is when x is 6.<br>
So we have a downward opening parabola, with vertex (maximum value) at (6,1). That means the function is increasing for x<6 and decreasing for x>6.