Question

How is the graph of the parent function y=x^2 transformed to produce the graph of y=3(x+1)^2?

Answer 1

Shift 1 units towards left and then stretch vertically 3 times.

Explanation:

We are given that a parent function

`y=x^2`

After transformation, we get a graph
`y=3(x+1)^2`

We have to find that how the parent function transformed to produce the graph of
`y=3(x+1)^2`

The parent graph is shifted 1 unit towards left by the rule of transformation

`f(x)\rightarrow f(x+1)`

By applying this rule then, we get

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

Now, the parent function stretched vertically 3 times the previous graph by the rule

`f(x)\rightarrow 3f(x)`

Apply this rule then, we get

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