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Question 157349: Find the vertex, the line of symmetry, and the maximum or minimum value of f(x).
f(x)=1/4(x+7)^2+3
Vertex is ? (type an ordered pair)
Line of symmetry is ?
Maximum/minimum value of f(x)
Is the vlue f(-7)=3 a minimum or maximum?: Find the vertex, the line of symmetry, and the maximum or minimum value of f(x).
f(x)=1/4(x+7)^2+3
Vertex is ? (type an ordered pair)
Line of symmetry is ?
Maximum/minimum value of f(x)
Is the vlue f(-7)=3 a minimum or maximum?
Answer by jim_thompson5910(9926) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=(1/4)(x+7)^2+3 Start with the given function



f(x)=(1/4)(x-(-7))^2+3 Rewrite x+7 as x-(-7)


Notice how the equation is now in vertex form f(x)=a(x-h)^2+k where a=1/4, h=-7 and k=3. Remember the vertex is (h,k). So the vertex is (-7,3).


Since the Line of symmetry is simply vertical line through the x-coordinate of the vertex, this means that the Line of symmetry is x=-7


Remember, the max/min is ALWAYS at the vertex (since the vertex is the highest/lowest point). So the max/min value of f(x) is f(x)=3


Since we know that a=1/4 this means that a>0. Since a>0, this means that the graph opens upward and there is a lowest point (which is the vertex). So the value f(-7)=3 is a minimum