Question
y = 2(x+2)^2 which of the following functions is a reflection of the starting function about the origin
y =-2(x+2)^2
y =2(-x*2)^2
y = -2(-x+2)^2
y =2(x+2)^2
y =-2(x+2)^2
y =2(-x*2)^2
y = -2(-x+2)^2
y =2(x+2)^2
Answers
GPT-4o mini
To find the reflection of the function \( y = 2(x + 2)^2 \) about the origin, we need to apply the transformations that reflect a function across the origin. This involves negating both the x and the y values.
1. Start with the original function:
\( y = 2(x + 2)^2 \)
2. Reflecting across the origin means replacing \( x \) with \( -x \) and \( y \) with \( -y \):
So, we replace \( y \) with \( -y \) and \( x \) with \( -x \):
\[
-y = 2(-x + 2)^2
\]
Rearranging gives:
\[
y = -2(-x + 2)^2
\]
Now, let's compare this derived reflection with the given options:
1. \( y = -2(x + 2)^2 \)
2. \( y = 2(-x \cdot 2)^2 \)
3. \( y = -2(-x + 2)^2 \)
4. \( y = 2(x + 2)^2 \)
From our calculations, the correct option that represents the reflection of the original function about the origin is:
**\( y = -2(-x + 2)^2 \)** (option 3).
1. Start with the original function:
\( y = 2(x + 2)^2 \)
2. Reflecting across the origin means replacing \( x \) with \( -x \) and \( y \) with \( -y \):
So, we replace \( y \) with \( -y \) and \( x \) with \( -x \):
\[
-y = 2(-x + 2)^2
\]
Rearranging gives:
\[
y = -2(-x + 2)^2
\]
Now, let's compare this derived reflection with the given options:
1. \( y = -2(x + 2)^2 \)
2. \( y = 2(-x \cdot 2)^2 \)
3. \( y = -2(-x + 2)^2 \)
4. \( y = 2(x + 2)^2 \)
From our calculations, the correct option that represents the reflection of the original function about the origin is:
**\( y = -2(-x + 2)^2 \)** (option 3).