In Problems 7–18, match each graph to one of the following functions:

$$\begin{gathered} \mathit{A}\mathbf{.}y=x^2+2\mathit{B}\mathbf{.}y=-x^2+2\mathit{C}.y=\left|x\right|+2 \\ \mathit{D}\mathbf{.}y=-\left|x\right|+2\mathit{E}\mathbf{.}y={(x-2)}^2\mathit{F}\mathbf{.}y=-{(x+2)}^2 \\ \mathit{G}\mathbf{.}y=\left|x-2\right|\mathit{H}\mathbf{.}y=-\left|x+2\right|\mathit{I}\mathbf{.}y=2x^2 \\ \mathit{J}\mathbf{.}y=-2x^2\mathit{K}\mathbf{.}y=2\left|x\right|\mathit{L}\mathbf{.}y=-2\left|x\right| \end{gathered}$$

There is the given graph we have to match each graph to its functions.

The given graph is similar to the graph of $y=x^2$ but it is a reflection of the function in the x-axis and it is vertically stretched by a factor of $2.$

When the right side of the function $y=f\left(x\right)$is multiplied by $-1$the graph of the new function $y=-f\left(x\right)$is the reflection about the x-axis of the graph of the function$y=f\left(x\right).$

Hence the function whose graph is the reflection of the graph of $y=x^2$in the x-axis is$y=-x^2.$

When the right side of a function $y=f\left(x\right)$ is multiplied by a positive number a, the graph of the new function $y=af\left(x\right)$ is obtained by multiplying each y-coordinate on the graph of $y=f\left(x\right)$ by a. The new graph is a vertically stretched $(ifa>1)$version of the graph of $y=f\left(x\right).$

Thus, the function of the graph is $y=-2x^2$that matched to option J.