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{{ printedBook.courseTrack.name }} {{ printedBook.name }} To match the function with its graph, we should first identify the vertex and then determine whether the parabola opens *upward* or *downward*. To do so, we will first express it in vertex form where $a,$ $h,$ and $k$ are either positive or negative numbers.
$y=-(x+1)_{2}+1⇔y=-1(x−(-1))_{2}+1 $
Let's compare the general formula for the vertex form with our equation.
$General formula:y=Equation:y= -a(x−-(h)_{2}+--k-1(x−(-1))_{2}+1 $
We can see that $a=-1,$ $h=-1,$ and $k=1.$ Since the vertex of a quadratic function written in vertex form is the point $(h,k),$ the vertex of our function is $(-1,1).$ Let's now determine the direction of the parabola. Recall that if $a>0,$ the parabola opens *upwards.* Conversely, if $a<0,$ the parabola opens *downwards.*

In the given function, we have $a=-1,$ which is *less than* $0.$ Therefore, the parabola opens *downward*. As a result, the graph of the function is the graph given in choice **D**.