What is the change that occurs to the parent function f(x) = x^2 given the function f(x) = 2(x + 2)^2 + 1.The graph is compressed by a factor of 2, moves 2 units to the right, and 1 unit up.The graph is compressed by a factor of 2, moves 2 units to the left, and 1 unit up.The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.The graph is stretched by a factor of 2, moves 2 units to the right, and 1 unit up.

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>1Looking wider is termed a compression.This happens when 0<a<1We 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 upTherefore the last choice is the correct answer.