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Given f (x) = - x2 + 6 x -11 determine each of the following.
(a) f ( 2)
(b) f ( -10)
(c) f (t )
Solution
(a) f ( 2) = - ( 2)2 + 6(2) -11 = -3
(b) f ( -10) = - ( -10)2 + 6 ( -10) -11 = -100 - 60 -11 ) -171
Be careful while squaring negative numbers!
(c ) f (t ) = -t 2 + 6t -11
Recall that we substitute for the x's whatever is in the parenthesis on the left. Frequently this will be something other than a number. Thus, in this case we put t's into for all the x's on the left.
In figure, the incircle of triangle ABC touches the sides BC, CA, and AB at D, E, and F respectively. Show that AF+BD+CE=AE+BF+CD= 1/2 (perimeter of triangle ABC), Ans:
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