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

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