Answer:
The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.
Step-by-step explanation:
The base of the quadratic function is
![f(x) = {x}^{2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7Bx%7D%5E%7B2%7D%20)
We can transform this function to look narrower or wider.
Looking narrower is termed a stretch.
This happens when a>1
Looking wider is termed a compression.
This happens when 0<a<1
We can also
![g(x) = a {(x + h)}^{2} + k](https://tex.z-dn.net/?f=g%28x%29%20%3D%20a%20%7B%28x%20%20%20%2B%20h%29%7D%5E%7B2%7D%20%20%2B%20k)
+h moves the parent graph to the left by h units
-h moves the parent graph to the left by h units.
+ k moves the parent function up by k units
- k moves the parent function down by k units.
The change that occurs to
![f(x) = {x}^{2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7Bx%7D%5E%7B2%7D%20)
given
![f(x) = 2( {x + 2)}^{2} + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%28%20%7Bx%20%20%2B%202%29%7D%5E%7B2%7D%20%20%2B%201)
is that, the graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up
Therefore the last choice is the correct answer.