SOLUTION: 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 valu

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?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given function

Rewrite as

Notice how the equation is now in vertex form where , and . 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

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

Since we know that this means that . Since , 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
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