SOLUTION: Find the x and y coordinates of the vertex {{{f(x)=-2x^2+2x+6}}}

Algebra ->  Graphs -> SOLUTION: Find the x and y coordinates of the vertex {{{f(x)=-2x^2+2x+6}}}      Log On


   

Question 131896: Find the x and y coordinates of the vertex f%28x%29=-2x%5E2%2B2x%2B6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-coordinate of the vertex, we can use this formula:

x=-b%2F%282a%29


From the equation f%28x%29=-2x%5E2%2B2x%2B6 we can see that a=-2 and b=2

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


x=%28-2%29%2F-4 Multiply 2 and -2 to get -4



x=1%2F2 Reduce


So the x-coordinate of the vertex is x=1%2F2.


This also means that the line of symmetry is x=1%2F2.


Now lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%281%2F2%29

f%28x%29=-2x%5E2%2B2x%2B6 Start with the given polynomial


f%281%2F2%29=-2%281%2F2%29%5E2%2B2%281%2F2%29%2B6 Plug in x=1%2F2


f%281%2F2%29=-2%281%2F4%29%2B2%281%2F2%29%2B6 Square 1%2F2 to get 1%2F4


f%281%2F2%29=-1%2F2%2B2%281%2F2%29%2B6 Multiply -2 by 1%2F4 to get -1%2F2


f%281%2F2%29=-1%2F2%2B1%2B6 Multiply 2 by 1%2F2 to get 1


f%281%2F2%29=13%2F2 Combine like terms


So the vertex is



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Answer:

This means that the x-coordinate of the vertex is and the y-coordinate of the vertex is