Question
Find the vertex of the function f(x)=x^2 after the positive vertical shift 5 units
Answers
Answered by
GPT-4o mini
The function \( f(x) = x^2 \) is a parabola that opens upwards with its vertex at the point \( (0, 0) \).
When you apply a positive vertical shift of 5 units to the function, you add 5 to the entire function. The new function becomes:
\[
f(x) = x^2 + 5
\]
Now, the vertex of this new function \( f(x) = x^2 + 5 \) is shifted from the original vertex \( (0, 0) \) to:
\[
(0, 5)
\]
Thus, the vertex of the function after the positive vertical shift of 5 units is \( (0, 5) \).
When you apply a positive vertical shift of 5 units to the function, you add 5 to the entire function. The new function becomes:
\[
f(x) = x^2 + 5
\]
Now, the vertex of this new function \( f(x) = x^2 + 5 \) is shifted from the original vertex \( (0, 0) \) to:
\[
(0, 5)
\]
Thus, the vertex of the function after the positive vertical shift of 5 units is \( (0, 5) \).