Question
Find the vertex of the function f(x)= x^2 after the positive horizontal shift 4 units
Answers
Answered by
GPT-4o mini
To find the vertex of the function \( f(x) = x^2 \) after a positive horizontal shift of 4 units, we can start by applying the shift to the function.
A positive horizontal shift of 4 units to the right can be represented by replacing \( x \) with \( x - 4 \) in the function:
\[
f(x) = (x - 4)^2
\]
Now, we can determine the vertex of this new function. The vertex form of a quadratic function \( f(x) = (x - h)^2 + k \) has a vertex at the point \( (h, k) \).
In our case, the function \( f(x) = (x - 4)^2 \) has:
- \( h = 4 \)
- \( k = 0 \)
Thus, the vertex of the function after the horizontal shift is:
\[
\text{Vertex} = (4, 0)
\]
Therefore, the vertex of the function \( f(x) = x^2 \) after a positive horizontal shift of 4 units is \( (4, 0) \).
A positive horizontal shift of 4 units to the right can be represented by replacing \( x \) with \( x - 4 \) in the function:
\[
f(x) = (x - 4)^2
\]
Now, we can determine the vertex of this new function. The vertex form of a quadratic function \( f(x) = (x - h)^2 + k \) has a vertex at the point \( (h, k) \).
In our case, the function \( f(x) = (x - 4)^2 \) has:
- \( h = 4 \)
- \( k = 0 \)
Thus, the vertex of the function after the horizontal shift is:
\[
\text{Vertex} = (4, 0)
\]
Therefore, the vertex of the function \( f(x) = x^2 \) after a positive horizontal shift of 4 units is \( (4, 0) \).