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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Let's start with analyzing the given function.
$f(x)=-2x_{2}+8x+5 $
The degree of the polynomial is $2,$ so the function is quadratic. Thus, the graph of the function is a parabola. Out of the given graphs, only **IV** shows a parabola. What is more, the leading coefficient is $-2,$ which is negative, so the ends of the function must go downwards. This is also true for the graph **IV**, so it is the answer.