Answer:
The graph of [tex]y=3(x+1)^2[/tex] can transformed by the parent function [tex]y=x^2[/tex]. The graph of parent function will shift 1 unit left and vertically stretched by factor 3.
Step-by-step explanation:
The parent function is
[tex]y=x^2[/tex]
This function can be transformed as
[tex]y=a(x+b)^2+c[/tex]
Where a represents vertical stretch and compression, b represents horizontal shift and c represents vertical shift.
If a>0, then it shows vertical stretch and if a<0 then it shows vertical compression.
If b>0, then the graph of parent function shifts left by b units and if b<0 then the graph of parent function shifts right by b units.
If x>0, then the graph of parent function shifts upward by c units and if c<0 then the graph of parent function shifts downward by c units.
The given function is
[tex]y=3(x+1)^2[/tex]
The value of a,b and c are 3, 1 and 0 respectively.
Therefore the graph of parent function will shift 1 unit left and vertically stretched by factor 3.
