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# The graph above is the graph of y=x2 translated and reflected in the xy-plane. Find an equation for this graph.

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The graph above is the graph of y=x2y=x2 translated and reflected in the xyxy-plane. Find an equation for this graph.

Sep 26, 2019

#1
+23866
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The graph above is the graph of $$y=x^2$$ translated and reflected in the xy-plane.
Find an equation for this graph.

1. translated

$$\begin{array}{|rcll|} \hline y_0 &=& x_0^2 \\ && \boxed{y = y_0+2\\ x=x_0+7 } \\ (y-2) &=& (x-7)^2 \\ y &=& 2 + (x-7)^2 \quad \text{ after translation} \\ \hline \end{array}$$

2. reflected

$$\begin{array}{|rcll|} \hline y_0 &=& 2 + (x_0-7)^2 \\ && \boxed{y = -y_0\\ x=x_0 } \\ -y &=& 2+(x-7)^2 \\ \mathbf{y} &=& \mathbf{-2-(x-7)^2} \quad \text{ after translation and reflextion} \\ \hline \end{array}$$

Sep 26, 2019
#2
+136
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Thank you so much!

Roxettna  Sep 29, 2019