Question

the graph of g(x) = (x + 2)² is a translation of the graph of f(x) ✔ left ✔ by 2 ✔ units. complete the graph of h(x) = (x − 3)² is a translation of the graph of f(x) dropdown by blank units. done ✔

Explanation:

Step1: Recall Translation Rule

For a function \( f(x) = x^2 \), the transformation \( f(x - h)=(x - h)^2 \) shifts the graph horizontally. If \( h>0 \), it shifts right by \( h \) units; if \( h<0 \), it shifts left by \( |h| \) units.

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

Here, comparing with \( f(x)=x^2 \), we have \( h = 3 \) (since \( h(x)=f(x - 3) \)). So the graph of \( h(x) \) is a translation of \( f(x) \) right by 3 units.

Answer:

The first dropdown: right; The second box: 3