Question

Could you please tell me the answers to these and how you get to them?

Answer 1

Given function to graph is,

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

To graph the above function using the transformation on the parent function y=x^2

The parent graph y=x^2 is given by,

by the transformation,

`\begin{gathered} y=(x+1)^2 \\ y=(x-(-1))^2 \end{gathered}`

The parent graph shift to left by 1 unit. (negative 1 makes it to shift left by 1 unit)

and the required equation is,

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

The transformed graph above is shifted up by 3 units.

The required graph is plotted as,

Hence the required graph.