SOLUTION: Find the vertex and the axis of symmetry for the following graph: {{{f(x)=3x^2-24x+51}}}

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Question 131104: Find the vertex and the axis of symmetry for the following graph:



Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
To find the vertex, we first need to find the line of symmetry (ie the x-coordinate of the vertex)
To find the line of symmetry, use this formula:



From the equation we can see that a=3 and b=-24

Plug in b=-24 and a=3


Negate -24 to get 24


Multiply 2 and 3 to get 6



Reduce


So the line of symmetry is


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 4 to the second power to get 16


Multiply 3 by 16 to get 48


Multiply 24 by 4 to get 96


Now combine like terms


So the vertex is (4,3)




-----------------------

Answer:


So the line of symmetry is and the vertex is (4,3)



If we graph, we can visually verify our answer

Graph of with the line of symmetry and the vertex (4,3)

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