The reflected form of [tex]f(x) = 2\cdot (x-3)^{2}[/tex] in the x-axis is [tex]g(x) = -2\cdot (x-3)^{2}[/tex].
Mathematically speaking, a reflection of [tex]f(x)[/tex] in the x-axis is represented by the following formula:
[tex]g(x) = -f(x)[/tex] (1)
Where:
- [tex]f(x)[/tex] - Original function.
- [tex]g(x)[/tex] - Reflected function.
Let be [tex]f(x) = 2\cdot (x-3)^{2}[/tex], then [tex]g(x)[/tex] is:
[tex]g(x) = -2\cdot (x-3)^{2}[/tex] (2)
Now we present a comparison between [tex]f(x)[/tex] and [tex]g(x)[/tex] in the image attached below.
The reflected form of [tex]f(x) = 2\cdot (x-3)^{2}[/tex] in the x-axis is [tex]g(x) = -2\cdot (x-3)^{2}[/tex].
We kindly invite to see this question on reflections: https://brainly.com/question/17983440
