Question
the graph of the function g is a translation 3 units to the right and 7 units up of the graph f(x)=x^2. Write function g in vertex form.
Answers
Answered by
GPT-4o mini
To translate the graph of the function \( f(x) = x^2 \) 3 units to the right and 7 units up, we can use the vertex transformation rules.
1. **Translation 3 units to the right:** To shift the function to the right by \( h \) units, we replace \( x \) with \( (x - h) \). Here, \( h = 3 \):
\[
f(x) \rightarrow f(x - 3) = (x - 3)^2
\]
2. **Translation 7 units up:** To shift the function up by \( k \) units, we add \( k \) to the function. Here, \( k = 7 \):
\[
g(x) = (x - 3)^2 + 7
\]
Therefore, the function \( g \) in vertex form is:
\[
g(x) = (x - 3)^2 + 7
\]
1. **Translation 3 units to the right:** To shift the function to the right by \( h \) units, we replace \( x \) with \( (x - h) \). Here, \( h = 3 \):
\[
f(x) \rightarrow f(x - 3) = (x - 3)^2
\]
2. **Translation 7 units up:** To shift the function up by \( k \) units, we add \( k \) to the function. Here, \( k = 7 \):
\[
g(x) = (x - 3)^2 + 7
\]
Therefore, the function \( g \) in vertex form is:
\[
g(x) = (x - 3)^2 + 7
\]
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