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

Algebra ->  Coordinate-system -> 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      Log On


   

Question 103996: 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
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the axis of symmetry, use this formula:

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

From the equation y=2x%5E2%2B4x-5 we can see that a=2 and b=4

x=%28-4%29%2F%282%2A2%29 Plug in b=4 and a=2


x=%28-4%29%2F4 Multiply 2 and 2 to get 4



x=-1 Reduce


So the axis of symmetry is x=-1


So the x-coordinate of the vertex is x=-1. Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%28-1%29

f%28x%29=2x%5E2%2B4x-5 Start with the given polynomial


f%28-1%29=2%28-1%29%5E2%2B4%28-1%29-5 Plug in x=-1


f%28-1%29=2%281%29%2B4%28-1%29-5 Raise -1 to the second power to get 1


f%28-1%29=2%2B4%28-1%29-5 Multiply 2 by 1 to get 2


f%28-1%29=2%2B-4-5 Multiply 4 by -1 to get -4


f%28-1%29=-7 Now combine like terms


So the vertex is (-1,-7)



Notice if you graph the equation y=2x%5E2%2B4x-5 you get



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