Which value of x gives the greatest value of "-x^2+8x-6"
There are 2 methods of solving this: completing the square or calculus, which makes this a versatile question for both GCSE and A Level students. It is also fairly simple to adapt.
Using calculus, the equation can be differentiated and then set equal to 0 to find that -2x + 8 = 0 and rearranged to find x = 4. If required in the session, the question can be extended to proving that this is a maxima by finding the second differential and saying that it is less than 0 so a maximum turning point.
Using completing the square: the equation can be re-arranged to find that the equation is -(x-4)2 +10 from which the answer can be read off and the reasons for this discussed
TD
