SOLUTION: Identify the vertex of the parabola defined by y = 2x(squared)+8x+9

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To find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)
To find the axis of symmetry, use this formula:



From the equation we can see that a=2 and b=8

Plug in b=8 and a=2


Multiply 2 and 2 to get 4



Reduce


So the axis 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 -2 to the second power to get 4


Multiply 2 by 4 to get 8


Multiply 8 by -2 to get -16


Now combine like terms


So the vertex is (-2,1)


Notice if you graph the equation you can see that the vertex is (-2,1). So this visually verifies our answer.