The function g(x) is [tex]\rm g(x) = -4x^2\\[/tex].
Given that,
The function g(x) is a transformation of the quadratic parent function,
[tex]\rm f(x) = x^2[/tex]
We have to determine,
What function is g(x)?
According to the question,
The function f(x) is a transformation of the quadratic parent function,
[tex]\rm f(x) = x^2[/tex]
In the given figure the function g(x) reflect across the x-axis and is vertically stretched by a scale factor of 'k',
Then, The function g(x) is,
[tex]\rm g(x) = -kx^2[/tex]
Therefore,
The quadratic equation passes through the point (1,4),
[tex]\rm g(x) = -kx^2\\\\g(1) = -k(1)^2\\\\-4 = -k\\\\k= 4[/tex]
Therefore,
The function g(x) is,
[tex]\rm g(x) = -kx^2\\\\g(x) = -4x^2[/tex]
Hence, The required function g(x) is [tex]\rm g(x) = -4x^2\\[/tex].
For more details refer to the link given below.
https://brainly.com/question/411998
