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.
g(x)=
Write your answer in the form a(x–h)2+k, where a, h, and k are integers or simplified fractions.
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 identify how the function \( g(x) \) has been transformed from the parent function \( f(x) \).
The general form of a transformed quadratic function is:
\[
g(x) = a(x - h)^2 + k
\]
Where:
- \( a \) determines the vertical stretch or compression and reflects the graph if negative,
- \( h \) represents the horizontal translation,
- \( k \) represents the vertical translation.
Without seeing the graph, I can provide you with the steps you need to follow to deduce \( a \), \( h \), and \( k \):
1. **Identify the Vertex**: Look at the graph of \( g(x) \) to determine the vertex, which will be the point \( (h, k) \).
2. **Compare the Width of the Parabolas**: Determine whether the graph of \( g(x) \) is narrower or wider than that of \( f(x) \). If it's narrower, \( |a| > 1 \). If it's wider, \( |a| < 1 \).
3. **Determine the Direction**: Check whether the parabola opens upwards or downwards to set the sign of \( a \).
4. **Substitute Values**: If you have specific points on the graph of \( g(x) \), you can plug them into the form to solve for \( a \).
Once you have identified \( a \), \( h \), and \( k \), plug them into the formula:
\[
g(x) = a(x - h)^2 + k
\]
If you provide the vertex and any points or features from the graph of \( g(x) \), I can help you insert those values into the function rule.
The general form of a transformed quadratic function is:
\[
g(x) = a(x - h)^2 + k
\]
Where:
- \( a \) determines the vertical stretch or compression and reflects the graph if negative,
- \( h \) represents the horizontal translation,
- \( k \) represents the vertical translation.
Without seeing the graph, I can provide you with the steps you need to follow to deduce \( a \), \( h \), and \( k \):
1. **Identify the Vertex**: Look at the graph of \( g(x) \) to determine the vertex, which will be the point \( (h, k) \).
2. **Compare the Width of the Parabolas**: Determine whether the graph of \( g(x) \) is narrower or wider than that of \( f(x) \). If it's narrower, \( |a| > 1 \). If it's wider, \( |a| < 1 \).
3. **Determine the Direction**: Check whether the parabola opens upwards or downwards to set the sign of \( a \).
4. **Substitute Values**: If you have specific points on the graph of \( g(x) \), you can plug them into the form to solve for \( a \).
Once you have identified \( a \), \( h \), and \( k \), plug them into the formula:
\[
g(x) = a(x - h)^2 + k
\]
If you provide the vertex and any points or features from the graph of \( g(x) \), I can help you insert those values into the function rule.