Question
The graph shows g(x), which is a translation of f(x)=x2. Write the function rule for g(x). Write your answer in the form a(x–h)2+k, where a, h, and k are integers or simplified fractions. went right 9
g(x)=
g(x)=
Answers
GPT-4o mini
To write the function rule for \( g(x) \) as a translation of \( f(x) = x^2 \), we need to consider that the function has been translated to the right by 9 units.
The general form of a vertically and horizontally translated quadratic function is given by:
\[
g(x) = a(x - h)^2 + k
\]
where:
- \( a \) is a scaling factor that affects the direction and width of the parabola,
- \( h \) is the horizontal translation (the amount we move left or right), and
- \( k \) is the vertical translation (the amount we move up or down).
Since the function has been translated to the right by 9 units, we set \( h = 9 \). If there is no vertical translation, we set \( k = 0 \). Assuming \( a = 1 \) (no vertical stretching or flipping), the function would be:
\[
g(x) = 1(x - 9)^2 + 0
\]
This simplifies to:
\[
g(x) = (x - 9)^2
\]
If you need a different value for \( a \) or there is additional vertical translation (which could add or subtract from the output), you would need that information to specify \( a \) and \( k \).
Thus, the simplest assumption without further information is:
\[
g(x) = (x - 9)^2
\]
If you have specific values for \( a \) or \( k \), please provide them for a more accurate equation.
The general form of a vertically and horizontally translated quadratic function is given by:
\[
g(x) = a(x - h)^2 + k
\]
where:
- \( a \) is a scaling factor that affects the direction and width of the parabola,
- \( h \) is the horizontal translation (the amount we move left or right), and
- \( k \) is the vertical translation (the amount we move up or down).
Since the function has been translated to the right by 9 units, we set \( h = 9 \). If there is no vertical translation, we set \( k = 0 \). Assuming \( a = 1 \) (no vertical stretching or flipping), the function would be:
\[
g(x) = 1(x - 9)^2 + 0
\]
This simplifies to:
\[
g(x) = (x - 9)^2
\]
If you need a different value for \( a \) or there is additional vertical translation (which could add or subtract from the output), you would need that information to specify \( a \) and \( k \).
Thus, the simplest assumption without further information is:
\[
g(x) = (x - 9)^2
\]
If you have specific values for \( a \) or \( k \), please provide them for a more accurate equation.