SOLUTION: Hello, I need help finding the equation of the axis of symmetry and the coordinates of the vertex of the graph of: y=2x^2+4x-5 Thank you

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To find the axis of symmetry, use this formula:



From the equation we can see that a=2 and b=4

Plug in b=4 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 -1 to the second power to get 1


Multiply 2 by 1 to get 2


Multiply 4 by -1 to get -4


Now combine like terms


So the vertex is (-1,-7)



Notice if you graph the equation you get



and you can see that the vertex is (-1,-7)