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

Question 113934: Identify the vertex of the parabola defined by y = 2x(squared)+8x+9
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 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.

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