Pregunta
\begin{tabular}{l} TYPE OUT THE EQUATION * \\ Write the Transformed equation given the following transformations of \( y=x^{2} \) \\ Translated left 6 and up 3 \\ Nour answer \\ \hline\end{tabular}
Ask by John Fuentes. in the United States
Jan 23,2025
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Transformed equation: \( y = (x + 6)^2 + 3 \)
Solución
Certainly! When transforming the equation \( y = x^{2} \) by translating it **left 6 units** and **up 3 units**, follow these steps:
1. **Translate Left 6 Units:**
To move the graph left, replace \( x \) with \( x + 6 \).
\( y = (x + 6)^{2} \)
2. **Translate Up 3 Units:**
To move the graph up, add 3 to the entire equation.
\( y = (x + 6)^{2} + 3 \)
**Transformed Equation:**
\[ y = (x + 6)^{2} + 3 \]
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Simplifique esta solución The Deep Dive
To find the transformed equation of \( y = x^{2} \) after applying the given transformations, we need to translate it left by 6 units and up by 3 units. The left translation changes the variable \( x \) to \( (x + 6) \), and the upward translation adds 3 to the entire equation. Thus, the transformed equation becomes: \[ y = (x + 6)^{2} + 3 \] Now you have the modified equation ready to show off your transformation skills!
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