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

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Question 90260This 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!
Are you sure it's not the minimum? No maximum occurs on the graph of y=x%5E2%2B6x. Well here's the solution to find the minimum

The minimum 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%2A1%29 Plug in b=6 and a=1


x=%28-6%29%2F2 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%28-3%29

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


f%28-3%29=%28-3%29%5E2%2B6%28-3%29 Plug in x=-3


f%28-3%29=%289%29%2B6%28-3%29 Raise -3 to the second power to get 9


f%28-3%29=%289%29%2B-18 Multiply 6 by -3 to get -18


f%28-3%29=-9 Now combine like terms


So the vertex is (-3,-9)


So the minimum value is -9


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