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

Algebra ->  Rational-functions -> SOLUTION: Identify the vertex of the parabola defined by y = 2x(squared)+8x+9      Log On


   

Question 113934: Identify the vertex of the parabola defined by y = 2x(squared)+8x+9
Answer by jim_thompson5910(35256) About Me  (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:

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

From the equation y=2x%5E2%2B8x%2B9 we can see that a=2 and b=8

x=%28-8%29%2F%282%2A2%29 Plug in b=8 and a=2


x=%28-8%29%2F4 Multiply 2 and 2 to get 4



x=-2 Reduce


So the axis of symmetry is x=-2


So the x-coordinate of the vertex is x=-2. Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%28-2%29

f%28x%29=2x%5E2%2B8x%2B9 Start with the given polynomial


f%28-2%29=2%28-2%29%5E2%2B8%28-2%29%2B9 Plug in x=-2


f%28-2%29=2%284%29%2B8%28-2%29%2B9 Raise -2 to the second power to get 4


f%28-2%29=8%2B8%28-2%29%2B9 Multiply 2 by 4 to get 8


f%28-2%29=8%2B-16%2B9 Multiply 8 by -2 to get -16


f%28-2%29=1 Now combine like terms


So the vertex is (-2,1)


Notice if you graph the equation y=2x%5E2%2B8x%2B9 you can see that the vertex is (-2,1). So this visually verifies our answer.