Question 485722
a) Express the quadratic equation in standard form
b) Sketch the graph (I know how do do this)
c) Find its maximum or minimum value (What does this mean? The vertex?)
What I have so far:
Original equation: f(x)=2x-x^2
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a) Quadratic equations are parabolas of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. 
For given equation: 
y=-x^2+2x
completing the square
y=-(x^2-2x+1)+1
y=-(x-1)^2+1
vertex: (1,1)
The negative sign of the lead coefficient means that the parabola opens downwards, that is, it has a maximum value=1 (y-coordinate of vertex)
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see graph below as a visual check on the answers:
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{{{ graph( 300, 300, -10, 10, -10, 10,-x^2+2x) }}}