Question
Interpret the key features of the graph. What type of transformation occurred from the parent
function?
(1 point)
This is a vertical stretch of the parent function y = x
2 due to the changes in the y-coordinates of each
point.
This is a vertical stretch of the parent function y = x
2 due to the changes in the y-intercept.
This is a vertical stretch of the parent function y = x
2 due to the changes in the x-coordinates of each
point.
This is a vertical stretch of the parent function y = x
2 due to the changes in the x-intercept
function?
(1 point)
This is a vertical stretch of the parent function y = x
2 due to the changes in the y-coordinates of each
point.
This is a vertical stretch of the parent function y = x
2 due to the changes in the y-intercept.
This is a vertical stretch of the parent function y = x
2 due to the changes in the x-coordinates of each
point.
This is a vertical stretch of the parent function y = x
2 due to the changes in the x-intercept
Answers
Answered by
GPT-4o mini
To interpret the key features of the graph of the function \( y = x^2 \) and determine the type of transformation, we need to focus on what a vertical stretch means in the context of this quadratic function.
A vertical stretch occurs when the output (y-coordinates) of the function is multiplied by a factor greater than 1. For example, if we modify the parent function to \( y = kx^2 \) (where \( k > 1 \)), the graph will be stretched away from the x-axis, making it narrower compared to the original \( y = x^2 \) graph.
Given the options you've provided:
1. **This is a vertical stretch of the parent function y = x^2 due to the changes in the y-coordinates of each point.**
2. **This is a vertical stretch of the parent function y = x^2 due to the changes in the y-intercept.**
3. **This is a vertical stretch of the parent function y = x^2 due to the changes in the x-coordinates of each point.**
4. **This is a vertical stretch of the parent function y = x^2 due to the changes in the x-intercept.**
The correct interpretation of a vertical stretch in the context of \( y = x^2 \) is:
- **This is a vertical stretch of the parent function y = x^2 due to the changes in the y-coordinates of each point.**
This choice accurately describes how the transformation affects the graph: increases in the y-values (output) while the x-values (input) remain unchanged.
A vertical stretch occurs when the output (y-coordinates) of the function is multiplied by a factor greater than 1. For example, if we modify the parent function to \( y = kx^2 \) (where \( k > 1 \)), the graph will be stretched away from the x-axis, making it narrower compared to the original \( y = x^2 \) graph.
Given the options you've provided:
1. **This is a vertical stretch of the parent function y = x^2 due to the changes in the y-coordinates of each point.**
2. **This is a vertical stretch of the parent function y = x^2 due to the changes in the y-intercept.**
3. **This is a vertical stretch of the parent function y = x^2 due to the changes in the x-coordinates of each point.**
4. **This is a vertical stretch of the parent function y = x^2 due to the changes in the x-intercept.**
The correct interpretation of a vertical stretch in the context of \( y = x^2 \) is:
- **This is a vertical stretch of the parent function y = x^2 due to the changes in the y-coordinates of each point.**
This choice accurately describes how the transformation affects the graph: increases in the y-values (output) while the x-values (input) remain unchanged.