Question 403823
find the domain and range of the function f(x)= -x^2+5x-6

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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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{{{ graph( 300, 200, -6, 5, -5, 2, -x^2+5x-6) }}}