What is the graph of f(x)=3x-x^2 ?

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Answer 1 · 2018-03-11T21:33:00

graph{3x-x^2 [-10, 10, -5, 5]}

The parabola opens downward because of the negative sign in front of the #x^2#.

The #x#-intercepts are #(0,0)# and #(3,0)# because

#3x-x^2=0#

factored equals

#(x)(x-3)=0#

When each of the parenthetical expressions is set equal to zero, you get

#x=0" "# and #" "x=3#

The vertex is #(3/2, 9/4)# because the #x#-coordinate of the vertex is

#"x-coord. vertex" = -b/(2a)#

#= -(3)/(2(-1))=3/2#

Then, you plug #3/2# into the equation for #x# and get

#f(3/2) = 3(3/2)-(3/2)^2 = 9/4#