Question

which translation maps the vertex of the graph of the function $f(x)=x^2$ onto the vertex of the function $g(x)=x^2 + 2x + 1$? left 1 unit left 2 units right 1 unit right 2 units

Explanation:

Step1: Find vertex of $f(x)$

For $f(x)=x^2$, vertex is $(0,0)$.

Step2: Rewrite $g(x)$ in vertex form

$$g(x)=x^2+2x+1=(x+1)^2$$

Step3: Find vertex of $g(x)$

For $g(x)=(x+1)^2$, vertex is $(-1,0)$.

Step4: Determine translation direction

From $(0,0)$ to $(-1,0)$: shift left 1 unit.

Answer:

left 1 unit