Question
The graph shown below is after a transformation.
A parabola is drawn in a coordinate plane where the axes range from negative 10 to 10, both by 1-unit increments.
(2 points)
Write the parent function: y=
Write the transformed function: y=
A parabola is drawn in a coordinate plane where the axes range from negative 10 to 10, both by 1-unit increments.
(2 points)
Write the parent function: y=
Write the transformed function: y=
Answers
GPT-4o mini
To provide the parent function and the transformed function, I need to know the nature of the transformation applied to the parabolic graph. However, since the graph hasn't been visually presented here, I can provide you with general information on how to write these functions based on common transformations.
**Parent Function:**
The parent function of a parabola is given by:
\[
y = x^2
\]
**Transformed Function:**
Transformations can include shifts (translations), vertical or horizontal stretches/compressions, and reflections. Here are a few examples of each type of transformation:
1. **Vertical Shift:** If the parabola shifts up by \(k\), then the function becomes:
\[
y = x^2 + k
\]
If it shifts down by \(k\), then use:
\[
y = x^2 - k
\]
2. **Horizontal Shift:** If the parabola shifts right by \(h\), then the function becomes:
\[
y = (x - h)^2
\]
If it shifts left by \(h\), then use:
\[
y = (x + h)^2
\]
3. **Vertical Stretch/Compression:** If the parabola is vertically stretched by a factor of \(a\), then the function becomes:
\[
y = a(x^2)
\]
If compressed, \(0 < a < 1\), then it's still the same form.
4. **Reflection:** If there's a reflection over the x-axis, the function becomes:
\[
y = -x^2
\]
To combine these transformations, you would create a general transformation form:
\[
y = a(x - h)^2 + k
\]
Where \(a\) determines vertical stretching/compression and reflection, \((h, k)\) shifts the graph horizontally and vertically.
To write the specific transformed function, I would need details about the transformation, such as shifts or flips. If you can describe the transformation or characteristics of the graph (movement, direction, etc.), I could provide a specific transformed function.
**Parent Function:**
The parent function of a parabola is given by:
\[
y = x^2
\]
**Transformed Function:**
Transformations can include shifts (translations), vertical or horizontal stretches/compressions, and reflections. Here are a few examples of each type of transformation:
1. **Vertical Shift:** If the parabola shifts up by \(k\), then the function becomes:
\[
y = x^2 + k
\]
If it shifts down by \(k\), then use:
\[
y = x^2 - k
\]
2. **Horizontal Shift:** If the parabola shifts right by \(h\), then the function becomes:
\[
y = (x - h)^2
\]
If it shifts left by \(h\), then use:
\[
y = (x + h)^2
\]
3. **Vertical Stretch/Compression:** If the parabola is vertically stretched by a factor of \(a\), then the function becomes:
\[
y = a(x^2)
\]
If compressed, \(0 < a < 1\), then it's still the same form.
4. **Reflection:** If there's a reflection over the x-axis, the function becomes:
\[
y = -x^2
\]
To combine these transformations, you would create a general transformation form:
\[
y = a(x - h)^2 + k
\]
Where \(a\) determines vertical stretching/compression and reflection, \((h, k)\) shifts the graph horizontally and vertically.
To write the specific transformed function, I would need details about the transformation, such as shifts or flips. If you can describe the transformation or characteristics of the graph (movement, direction, etc.), I could provide a specific transformed function.