Bot GPT 4-o mini To find the transformation of the function \( f(x) = x^2 \) in the vertex form \( g(x) = a(x - h)^2 + k \), we will apply the specified translations and reflections. Here are the answers for each part:
#1: Translation 4 units left of \( f(x) = x^2 \)
Translating left involves adding to \( x \): \[ g(x) = (x + 4)^2 \]
#2: Translation 5 units up of \( f(x) = x^2 \)
Translating up involves adding to the entire function: \[ g(x) = x^2 + 5 \]
#3: Reflection across the x-axis of \( f(x) = x^2 \)
Reflecting across the x-axis involves changing the sign of the function: \[ g(x) = -x^2 \]
#4: Translation 2 units right and 1 unit down of \( f(x) = x^2 \)
Translating 2 units right means subtracting from \( x \) and translating 1 unit down means subtracting from the entire function: \[ g(x) = (x - 2)^2 - 1 \]
In summary:
- #1: \( g(x) = (x + 4)^2 \)
- #2: \( g(x) = x^2 + 5 \)
- #3: \( g(x) = -x^2 \)
- #4: \( g(x) = (x - 2)^2 - 1 \)
1 answer