State the various transformations applied to the base function ƒ(x) = x2 to obtain a graph of the functiong(x) = (x − 3)2 + 5.

The standard vertex form for a parabola is:
y = a(x - h)² + k
Anything in the parentheses is left or right depending on if is negative or positive and k is up or down.
Transformations:
- Translate Right 2 units. It is right because in the standard equation is x-h so h is positive when there is negative sign and negative when there is a positive sign
-Translate up 5 units

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MrRoyal MrRoyal · Answer 2 · 2022-07-15T12:35:15+02:00

The various transformations are 5 units up and 3 units left

How to determine the applied transformations?

The base function is given as:

f(x) = x^2

The new function is given as:

g(x) = (x - 3)^2 + 5

First, the base function is translated 3 units right.

This is represented as:

g(x) = f(x - 3)

So, we have:

g(x) = (x - 3)^2

Next, the base function is translated 5 units up.

This is represented as:

g(x) = f(x - 3) + 5

So, we have:

g(x) = (x - 3)^2 + 5

Hence, the various transformations are 5 units up and 3 units left