Question 110038
Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). 
y=-x^2+3x-3 
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Complete the square on the x-terms and keep the equation balanced:
-x^2+3x = y+3
-(x^2-3x+(3/2)^2) = y+3-(3/2)^2
-(x-(3/2))^2 = y+(3/4)
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Axis of Symmetry: x=(3/2)
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Table:
x=0, then y = -3
x=1, then y = -1
x=2, then y = -1
x=3, then y = -3
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Graph:
{{{graph(400,300,-10,10,-10,10,-x^2+3x-3)}}}
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Cheers,
Stan H.