Question

hich 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 $f(x)$

The vertex of $f(x)=x^2$ is at $(0, 0)$.

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

Complete the square for $g(x)=x^2+2x+1$:
$$g(x)=(x+1)^2$$

Step3: Identify vertex of $g(x)$

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

Step4: Determine translation direction/units

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

Answer:

left 1 unit