Question 221378: Find the vertex, the line of symmetry, and the maximum or minimum value of f(x).
f(x)=-(x+8)^2-7
The vertex =
The line of symmetry =
The minimum or maximum value=
Is this maximum or minimum?
Thank you!
Answer by likaaka(51)   (Show Source):
You can put this solution on YOUR website! Your function is already set in standard parabola form y=a(x-h)^2+k, where (h,k) is your vertex
So given the equation,
f(x)=-(x+8)^2-7
The vertex: (-8, -7), since in the formula above, h is always negative, when the positive 8 is translated from the given equation the x-coordinate of the vertex must be negative
The line of symmetry: always written as x=h, x = -8
The minimum or maximum value: written as f(h)=k, f(-8) = -7
Is this maximum or minimum? if the graph opens up, the f(h)=k value is a minimum. if the graph open down, the f(h)=k value is a maximum. To determine the orientation of the graph look at a. If "a" is a positive, graph opens up; if "a" is a negative, graph opens down.
In other words...
positive a, graph opens up, f(h)=k is a minimum value
negative a, graph opens down, f(h)=k is a maximum value
In the given equation, a = -1, so f(-8) = -7 is a maximum value
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