SOLUTION: 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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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.

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