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The question asks which parent functions have a y-intercept that is the same as their vertex, and it provides the following options:

- Quadratic
- Square Root
- Cube Root
- Absolute Value
- Rational

Let's analyze each one:

1. **Quadratic**: The parent function for a quadratic equation is \( f(x) = x^2 \). The vertex of this function is at \( (0, 0) \), which is also the y-intercept. **(This is a correct choice)**

2. **Square Root**: The parent function for a square root equation is \( f(x) = \sqrt{x} \). The "vertex" of this function is at \( (0, 0) \), which is also the y-intercept. **(This is a correct choice)**

3. **Cube Root**: The parent function for a cube root equation is \( f(x) = \sqrt[3]{x} \). The vertex-like point (inflection point) is at \( (0, 0) \), and it is also the y-intercept. **(This is a correct choice)**

4. **Absolute Value**: The parent function for an absolute value equation is \( f(x) = |x| \). The vertex is at \( (0, 0) \), which is also the y-intercept. **(This is a correct choice)**

5. **Rational**: The parent function for a rational equation is \( f(x) = \frac{1}{x} \). This function does not have a vertex and does not have a y-intercept at the origin (or in some cases at all, depending on the context). **(This is not a correct choice)**

### Correct answers:
- Quadratic
- Square Root
- Cube Root
- Absolute Value

Do you have any questions or would you like further details?

### Related Questions:
1. What is the vertex form of a quadratic function and how does it relate to the y-intercept?
2. How do you determine the vertex of a square root function?
3. Can a rational function have a vertex? Why or why not?
4. What are the characteristics of the cube root function that differentiate it from quadratic functions?
5. How can transformations affect the location of the vertex and y-intercept of these functions?

### Tip:
For any parent function, the vertex (or equivalent critical point) often corresponds with the y-intercept when the function has its simplest form.

Which parent functions have a y-intercept that is the same as their vertex? Choose all that apply. Options include Quadratic, Square Root, Cube Root, Absolute Value, and Rational.

Explore which parent functions, including Quadratic, Square Root, Cube Root, Absolute Value, and Rational, have a y-intercept that coincides with their vertex. This problem is suitable for high school students in Grades 9-12.

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