SOLUTION: Could someone please show me how to get the line of symentry, vertex and the min/max of the line. {{{f(x)=(1/4)(x+2)^2+2}}}

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: Could someone please show me how to get the line of symentry, vertex and the min/max of the line. {{{f(x)=(1/4)(x+2)^2+2}}}      Log On

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Question 160400: Could someone please show me how to get the line of symentry, vertex and the min/max of the line.
f%28x%29=%281%2F4%29%28x%2B2%29%5E2%2B2
Found 2 solutions by Earlsdon, scott8148:
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Find the line of symmetry (sp!), vertex, and the min. or max. of the curve:
f%28x%29+=+%281%2F4%29%28x%2B2%29%5E2%2B2
Your quadratic equation is already written in the "vertex" form of:y+=+a%28x-h%29%5E2%2Bk where the vertex is located at the point (h, k), so you can write the coordinates of the vertex directly from your equation: (h = -2 and k = 2)
Vertex is at (-2, 2)
The line of symmetry is the vertical line that passes through the point x = -2, so the equation of the line of symmetry is: highlight%28x+=+-2%29.
The parabola represented by your equation open upwards which you can tell because the coefficient of x%5E2 i.e. (a+=+1%2F4) is positive, so the vertex is a minimum.
See the graph below:
graph%28400%2C400%2C-10%2C5%2C-2%2C10%2C%281%2F4%29%28x%2B2%29%5E2%2B2%29

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
this eqn is in the form y=a(x-h)^2+k (sometimes called the "vertex form")

the vertex is (h,k)

the axis of symmetry is x=h

the min/max is the vertex __ min if a is positive __ max if a is negative