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

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) (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:

Here is the general formula to find the x-value of the vertex

From the equation we can see that a=-1 and b=6

Plug in b=6 and a=-1

Multiply 2 and -1 to get -2

Reduce

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

Lets evaluate

Start with the given polynomial

Plug in

Raise 3 to the second power to get 9

Multiply 6 by 3 to get 18

Now combine like terms

So the vertex is (3,9)

So the maximum value is 9

If we graph , we can clearly see the maximum value

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