<u>Given</u>:
The given parent function is ![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
We need to determine the equation of the new translated (shifted) function g(x).
<u>Vertical stretch:</u>
The general rule to shift the graph f(x), to shift c units upward is ![g(x)=f(x)+c](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%29%2Bc)
From the graph, it is obvious that the graph f(x) is shifted 1 unit upwards.
Thus, applying the above rule, we get;
<u>Horizontal stretch:</u>
The general rule to shift the graph f(x) to shift c units to the left is ![g(x)=f(x+c)](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%2Bc%29)
From, the graph, it is obvious that the graph f(x) is shifted 2 units to the left.
Thus, applying the above rule, we have;
![g(x)=(x+2)^2](https://tex.z-dn.net/?f=g%28x%29%3D%28x%2B2%29%5E2)
<u>Equation of the new function g(x):</u>
From the figure, it is obvious that the graph g(x) is shifted 1 unit upwards and 2 units to the left.
Thus, we have;
![g(x)=(x+2)^2+1](https://tex.z-dn.net/?f=g%28x%29%3D%28x%2B2%29%5E2%2B1)
Therefore, the equation of the new function g(x) is ![g(x)=(x+2)^2+1](https://tex.z-dn.net/?f=g%28x%29%3D%28x%2B2%29%5E2%2B1)