<u>Given</u>:
The parent function is ![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
We need to determine the equation for the new function g(x)
<u>Vertical shift:</u>
From the graph, it is obvious that the parent function is shifted 6 units upwards.
The general rule to shift the graph c units upwards is ![f(x)+c](https://tex.z-dn.net/?f=f%28x%29%2Bc)
Thus, using the rule, the vertical shift of the new function g(x) is given by
![g(x)=x^2+6](https://tex.z-dn.net/?f=g%28x%29%3Dx%5E2%2B6)
<u>Horizontal shift:</u>
From the graph, it is obvious that the parent function is shifted 2 units to the right.
The general rule to shift the graph c units to the right is ![f(x-c)](https://tex.z-dn.net/?f=f%28x-c%29)
Thus, the horizontal shift of the new function g(x) is given by
![g(x)=(x-2)^2](https://tex.z-dn.net/?f=g%28x%29%3D%28x-2%29%5E2)
<u>Equation for the new function g(x):</u>
Since, the new function is shifted 2 units to the right and 6 units upward is given by the equation,
![g(x)=(x-2)^2+6](https://tex.z-dn.net/?f=g%28x%29%3D%28x-2%29%5E2%2B6)
Hence, the equation of the new function is ![g(x)=(x-2)^2+6](https://tex.z-dn.net/?f=g%28x%29%3D%28x-2%29%5E2%2B6)