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
[tex]f(x) = {x}^{2} [/tex]
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
[tex]g(x) = a {(x + h)}^{2} + k[/tex]
+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
[tex]f(x) = {x}^{2} [/tex]
given
[tex]f(x) = 2( {x + 2)}^{2} + 1[/tex]
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.
