Question 236217: find the vertex, the line of symmetry and the maximum or minimum value of f(x). Graph the function f(x)=1/2(x+6)^2+3
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the vertex, the line of symmetry and the maximum or minimum value of f(x). Graph the function f(x)=1/2(x+6)^2+3
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Vertex (-6,3)
Line of symmetry: x = -6
Minimum at the vertex is f(x)=3
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Cheers,
Stan H.
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
 
The equation
is
a parabola with a vertex at (h,k) and which passes
through the points (h+1,k+a) and (h-1,k+a), and its
axis of symmetry is the vertical line whose equation
is 
So in the problem:
 ,  , 
[Notice that the sign is changed for h but kept for k]
So the vertex is (h,k) or (-6,3),
The parabola passes through (h-1,k+a) and (h+1,k+a), or
(-6-1,3+ ) or (-7, ) and
(-6+1,3+) or (-5,)
Its axis of symmetry is the vertical line whose equation
is or 
We plot the vertex (-6,3)
We draw the axis of symmetry which is a vertical line
through the vertex (the green line below:
Then we plot the two points,
one on each side of the vertex
(-7,) and (-5,)
Finally we sketch in the parabola:
Edwin
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