Question

the graph of g(x) = x² + 2 is a translation of the graph of f(x) up by 2 units. complete the graph of h(x) = x² − 3 is a translation of the graph of f(x) by units. done

Explanation:

Step1: Recall Vertical Translation Rule

For a function \( f(x) = x^2 \), the vertical translation is given by \( f(x) + k \), where \( k>0 \) is up and \( k<0 \) is down.

Step2: Analyze \( h(x) = x^2 - 3 \)

Compare \( h(x)=x^2 - 3 \) with \( f(x)=x^2 \). Here, \( k=-3 \), so the translation is down by 3 units.

Answer:

down, 3