SOLUTION: Let f(x)=(x-2)^2+3. Describe a combination of different types of transformations of f that results in the original function. (What does "original function mean here? Parent or f(

Algebra ->  Functions -> SOLUTION: Let f(x)=(x-2)^2+3. Describe a combination of different types of transformations of f that results in the original function. (What does "original function mean here? Parent or f(      Log On


   

Question 1184496: Let f(x)=(x-2)^2+3. Describe a combination of different types of transformations of f that results in the original function.
(What does "original function mean here? Parent or f(x) as given?)
This question is from Big Ideas Math Algebra 2: 2022
Chapter 2
Section 2.1: Transformations of Quadratic Functions
Section 2.1: Practice (1 - 47), Question 46
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=x^2, base or original function.
(x-2) will shift the graph to the right 2 units.
+3 will shift the graph upward 3 units.
graph%28300%2C300%2C-5%2C5%2C-10%2C10%2Cx%5E2%2C%28x-2%29%5E2%2C%28x-2%29%5E2%2B3%29
The vertex for f(x)=(x-2)^2+3 is at (2, 3), changing the first sign and leaving the second sign as is.