SOLUTION: find the domain and range of the function f(x)= -x^2+5x-6

Question 403823: find the domain and range of the function f(x)= -x^2+5x-6
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the domain and range of the function f(x)= -x^2+5x-6
..
change f(x) to standard form of a parabola by completing the square,
y=(x-h)^2+k,(h,k) being the coordinates of the vertex
y=-(x^2-5x+25/4)-6+25/4
y=-(x-5/2)^2-24/4+25/4
y=-(x-5/2)^2+1/4
You can now see that this is a parabola that opens downward(because negative coefficient of x^2) with the vertex at (5/2,1/4)
This clearly shows that the domain is all real numbers or (-infinity,infinity)
and the range from (-infinity,1/4]
see the graph below:
..

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