Question
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?
right 1 unit
left 1 unit
right 2 units
left 2 units
right 1 unit
left 1 unit
right 2 units
left 2 units
Answers
GPT-4o mini
To find which translation maps the vertex of the graph of the function \( f(x) = x^2 \) onto the vertex of the function \( g(x) = x^2 + 2x + 1 \), we first need to identify the vertices of both functions.
1. The function \( f(x) = x^2 \) is in standard form, and its vertex is at the point \( (0, 0) \).
2. The function \( g(x) = x^2 + 2x + 1 \) can be rewritten in vertex form. To do this, we can complete the square:
\[
g(x) = x^2 + 2x + 1 = (x + 1)^2
\]
The vertex of \( g(x) \) is at \( (-1, 0) \).
Now we compare the vertices:
- Vertex of \( f(x) \) is \( (0, 0) \)
- Vertex of \( g(x) \) is \( (-1, 0) \)
To move from the vertex of \( f(x) \) at \( (0, 0) \) to the vertex of \( g(x) \) at \( (-1, 0) \), we need to translate left by 1 unit.
Therefore, the correct translation is **left 1 unit**.
1. The function \( f(x) = x^2 \) is in standard form, and its vertex is at the point \( (0, 0) \).
2. The function \( g(x) = x^2 + 2x + 1 \) can be rewritten in vertex form. To do this, we can complete the square:
\[
g(x) = x^2 + 2x + 1 = (x + 1)^2
\]
The vertex of \( g(x) \) is at \( (-1, 0) \).
Now we compare the vertices:
- Vertex of \( f(x) \) is \( (0, 0) \)
- Vertex of \( g(x) \) is \( (-1, 0) \)
To move from the vertex of \( f(x) \) at \( (0, 0) \) to the vertex of \( g(x) \) at \( (-1, 0) \), we need to translate left by 1 unit.
Therefore, the correct translation is **left 1 unit**.