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

Algebra ->  Average -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%281%2F4%29%28x%2B7%29%5E2%2B3 Start with the given function



f%28x%29=%281%2F4%29%28x-%28-7%29%29%5E2%2B3 Rewrite x%2B7 as x-%28-7%29


Notice how the equation is now in vertex form f%28x%29=a%28x-h%29%5E2%2Bk where a=1%2F4, 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%28x%29=3


Since we know that a=1%2F4 this means that a%3E0. Since a%3E0, 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