Question

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

Answer 1

The parent function is y = x^2

There is a compression of 3:

y = 3x^2

There is a shift by 1 unit to the left:

y = 3(x + 1)^2

Answer 2

D. Translated 1 unit to the left and vertically stretched by a factor of 3.

Explanation:

We are given the parent function,
`y=x^2`.

It is transformed to the function,
`y=3(x+1)^2`.

As we know,

Translation shifts the function in any direction.

Dilation stretches or shrinks the function along the axis.

From the function, we can see that,

The parent function
`y=x^2` is translated 1 unit to the left and vertically stretched by a factor of 3 to obtain the new function.

Hence, option D is correct.