SOLUTION: Find the maximum value of y=-x squared+6x

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Question 90267This question is from textbook
: Find the maximum value of y=-x squared+6x This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum value occurs at the vertex of the graph
First determine the x-value of the vertex:


x=-b%2F%282a%29 Here is the general formula to find the x-value of the vertex

From the equation y=-x%5E2%2B6x we can see that a=-1 and b=6

x=%28-6%29%2F%282%2A-1%29 Plug in b=6 and a=-1


x=%28-6%29%2F-2 Multiply 2 and -1 to get -2

x=3 Reduce



So the x-coordinate of the vertex is x=3. Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%283%29

f%28x%29=-x%5E2%2B6x Start with the given polynomial


f%283%29=-%283%29%5E2%2B6%283%29 Plug in x=3


f%283%29=-%289%29%2B6%283%29 Raise 3 to the second power to get 9


f%283%29=-%289%29%2B18 Multiply 6 by 3 to get 18


f%283%29=9 Now combine like terms


So the vertex is (3,9)


So the maximum value is 9


If we graph y=-x%5E2%2B6x, we can clearly see the maximum value