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Question
Transformation of Quadratic Functions

(1 point)
Write your answer in the form a(x−h)2+k

#1 Find g(x)
where g(x)
is the translation 4 units left of f(x)=x2
g(x) =
#2 Find g(x)
where g(x)
is the translation 5 units up of f(x)=x2
g(x) =
#3 Find g(x)
where g(x)
is the reflection across the x-axis of f(x)=x2
g(x) =
#4 Find g(x)
where g(x)
is the translation 2 units right and 1 unit down of f(x)=x2
g(x) =



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Answer 1

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:** \( g(x) = (x - 2)^2 - 1 \)