SOLUTION: find the axis of symmetry for this function: g(x)=(x^2/2)+4x+6 Vertex formula: -b/2a My Attempts: 1.) a= 1/2 b=4 c=6 AOS: -(4)/2(1/2) = -4 2.) 1/2(x^2+8x)+6 1/2(x^2+8x

Algebra ->  Graphs -> SOLUTION: find the axis of symmetry for this function: g(x)=(x^2/2)+4x+6 Vertex formula: -b/2a My Attempts: 1.) a= 1/2 b=4 c=6 AOS: -(4)/2(1/2) = -4 2.) 1/2(x^2+8x)+6 1/2(x^2+8x      Log On


   

Question 1206454: find the axis of symmetry for this function:
g(x)=(x^2/2)+4x+6
Vertex formula: -b/2a
My Attempts:
1.) a= 1/2 b=4 c=6
AOS: -(4)/2(1/2) = -4
2.) 1/2(x^2+8x)+6
1/2(x^2+8x-?+?)+6
I am not sure what to place here when using the factoring route. Apparently the vertex should be (-1,11/2) but I am not sure how they got that since I struggle with factoring.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
----------------------
2.)
1/2(x^2+8x)+6
1/2(x^2+8x-?+?)+6
----------------------


%281%2F2%29%28x%5E2%2B8x%29%2B6---------not the same function as your g(x).
%281%2F2%29x%5E2%2B4x%2B6
Axis of Symmetry, -b%2F%282a%29
-4%2F%282%281%2F2%29%29
highlight%28-4%29

graph%28400%2C400%2C-8%2C8%2C-8%2C8%2C%281%2F2%29x%5E2%2B4x%2B6%29
Without performing the algebra steps, vertex looks like (-4,-2).


The algebraic steps you would want would be equivalent to this:

y=%281%2F2%29%28x%5E2%2B8x%29%2B6
%281%2F2%29%28x%5E2%2B8x%2B4%5E2-4%5E2%29%2B6
%281%2F2%29%28%28x%2B4%29%5E2-4%5E2%29%2B6
%281%2F2%29%28%28x%2B4%29%5E2-16%29%2B6
%281%2F2%29%28x%2B4%29%5E2-8%2B6
%281%2F2%29%28x-%28-4%29%29%5E2-2
That now in vertex form.
%281%2F2%29%28x-highlight%28%28-4%29%29%29%5E2-highlight%282%29----------read vertex directly from the expression:
(-4,-2)