Question

The parabola LaTeX: f\left(x\right)=x^2f ( x ) = x 2 was translated up by 4 units.

What is the function rule for the new transformed parabola LaTeX: g\left(x\right)g ( x )?



Group of answer choices



LaTeX: g\left(x\right)=4x^2 g ( x ) = 4 x 2



LaTeX: g\left(x\right)=\left(x+4\right)^2 g ( x ) = ( x + 4 ) 2



LaTeX: g\left(x\right)=x^2+4 g ( x ) = x 2 + 4



LaTeX: g\left(x\right)=\left(x-4\right)^2 g ( x ) = ( x − 4 ) 2

Answer 1

C. g(x) = x²+4

Explanation:

Given the parabola function f(x) = x²

Translating the function up by 4 means adding the constant value of +4 to the function since it's translated along the positive y axis. The resulting function g(x) will be x²+4

Hence the correct answer is g(x) = x²+4. Option C is correct.