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{{ printedBook.courseTrack.name }} {{ printedBook.name }} To determine the quadratic function that is obtained from the parent function $f(x)=x_{2}$ after the given sequence of transformations, let's consider the transformations one at a time.

We'll start by performing a horizontal stretch of the parent function by a factor of $2.$ This is done by multiplying the $x$-variable by $21 .$ The resulting function is $y=21 x_{2}.$

Next, to perform a vertical translation $2$ units up we need to add $2$ to the whole function. The result is $y=21 x_{2}+2.$

Finally, let's reflect the function across the $y$-axis by multiplying the variable by $-1.$ $y=21 (-1⋅x)_{2}+2 $ This will not affect the graph since $(-x)_{2}=x_{2}.$

The quadratic function that is obtained after the sequence of transformations is $g(x)=21 x_{2}+2.$

The vertex of $g(x)$ let's rewrite it into vertex form. This is done by subtracting $0$ from $x.$ $g(x)=21 (x−0)_{2}+2 $ Therefore, the vertex of $g$ is $(0,2).$