SOLUTION: Hello, im really having trouble understanding my homework on the absolute maximum and minimum values of a function. The problem that i am on right now is g(x)= -x^2+2x+8. Thank yo

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Question 384053: Hello, im really having trouble understanding my homework on the absolute maximum and minimum values of a function. The problem that i am on right now is g(x)= -x^2+2x+8.
Thank you for your help in advance!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the max/min of a parabola is the vertex , which is on the axis of symmetry

general equation for the axis of symmetry ___ x = -b / (2a)

in this case ___ x = (-2) / (2 * (-1)) = (-2) / (-2) = 1

plug into the function to find the vertex ___ g(x) = -(1)^2 + 2(1) + 8 = 9 ___ the vertex is (1,9)

the coefficient of the squared term is negative , so the parabola opens downward

this means that the vertex is an absolute maximum