Y=x^2 given a vertical stretch with a factor of 3 then translated right 2 units.

Answer 1

To stretch a function f(x) by a factor h we simply multiply hf(x). To shift a function right by an amount b we want the value of f(a) at x = a to instead be at x = a + b. This means f(x) → f(x-b), since f(a+b-b) = f(a).

Answer 2

Hi Lidia!

In order to find the equation based on the transformations given, we have to find which transformations match up with which changes to the equation. The transformations are explained in the link below. For the vertical stretch of 3, we multiply the x^2 by 3 to get y=3x^2, and for the horizontal translation right 2 units we subtract 2 from the x to get y=3(x-2)^2.

https://www.onlinemathlearning.com/horizontal-vertical-stretch.html