Question

How is the graph of y=3(x+1)^2 related to its parent function, y=x^2

Answer 1

Horizontal translation left 1
Vertical stretch by 3

Answer 2

The graph of
`y=3(x+1)^2` can transformed by the parent function
`y=x^2`. The graph of parent function will shift 1 unit left and vertically stretched by factor 3.

Explanation:

The parent function is

`y=x^2`

This function can be transformed as

`y=a(x+b)^2+c`

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

`y=3(x+1)^2`

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.