Question

How to graph f(x)=(x-2)^2+3

Answer 1

Using translation concepts, the graph of f(x) = (x - 2)² + 3 is given at the end of the question.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, we have that the parent and the translated function are given, respectively, by:

• g(x) = x².

• f(x) = (x - 2)² + 3.

The translations are as follows:

• Right two units, as x -> x - 2.

• Up 3 units, because f(x) = g(x) + 3.

Hence the graphs are given at the end of the answer, with the parent function in red and the translated function f(x) = (x - 2)² + 3 in green.

More can be learned about translation concepts at brainly.com/question/4521517

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