Question

question the graph of $f(x) = -2x^2$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ down 1 unit.

Explanation:

Step1: Recall vertical shift rule

For a function \( y = f(x) \), shifting it down by \( k \) units ( \( k>0 \)) gives \( y = f(x)-k \).

Step2: Apply the rule to \( f(x) \)

Given \( f(x)=-2x^{2} \), to shift it down 1 unit, we subtract 1 from \( f(x) \). So \( g(x)=f(x)-1=-2x^{2}-1 \).

Answer:

\( g(x)=-2x^{2}-1 \)