SOLUTION: I am not sure which Algebra section this question fits under. Hopefully someone can help me figure this out. I am lost. I am trying to find the vertex of the function: f(x)=x

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am not sure which Algebra section this question fits under. Hopefully someone can help me figure this out. I am lost. I am trying to find the vertex of the function: f(x)=x      Log On


   

Question 112302: I am not sure which Algebra section this question fits under. Hopefully someone can help me figure this out. I am lost.
I am trying to find the vertex of the function:
f(x)=x^2 -8x -6
Thank you!
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=x%5E2-8x-6 we can see that a=1 and b=-8

x=%28--8%29%2F%282%2A1%29 Plug in b=-8 and a=1


x=8%2F%282%2A1%29 Negate -8 to get 8


x=%288%29%2F2 Multiply 2 and 1 to get 2



x=4 Reduce


So the axis of symmetry is x=4


So the x-coordinate of the vertex is x=4. Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%284%29

f%28x%29=x%5E2-8x-6 Start with the given polynomial


f%284%29=%284%29%5E2-8%284%29-6 Plug in x=4


f%284%29=%2816%29-8%284%29-6 Raise 4 to the second power to get 16


f%284%29=-22 Now combine like terms


So the vertex is (4,-22)


Notice if you graph the equation y=x%5E2-8x-6 you can see that the vertex is at (4,-22). So this verifies our answer.