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What is the domain and range and parent function

The graph shown is a parabola that opens upward. It resembles the graph of a basic quadratic function. Let's go through each part of the question:

### 1. **Parent Function:**
The parent function of this graph is a basic quadratic function:
\[
y = x^2
\]

### 2. **Domain (D):**
The domain of a quadratic function is all real numbers because the graph extends infinitely to the left and right. Therefore, the domain is:
\[
D: (-\infty, \infty)
\]

### 3. **Range (R):**
Since the parabola opens upwards and has its vertex at the minimum point, the range includes all values greater than or equal to the y-coordinate of the vertex. The vertex of this parabola appears to be at \( (0, -5) \). Therefore, the range is:
\[
R: [-5, \infty)
\]

Would you like more details or have any questions?

### 5 Relative Questions:
1. How do you determine the vertex of a quadratic function?
2. What is the effect of the coefficient of \(x^2\) on the direction the parabola opens?
3. How do you find the axis of symmetry for a parabola?
4. How does changing the vertex affect the range of a quadratic function?
5. What transformations can be applied to the parent function \(y = x^2\)?

### Tip:
The vertex form of a quadratic equation, \(y = a(x-h)^2 + k\), makes it easy to identify the vertex \((h, k)\) and the direction in which the parabola opens (upward if \(a > 0\) and downward if \(a < 0\)).

What is the domain and range and parent function of the parabola shown in the graph?

This article explains how to determine the domain, range, and parent function of a quadratic graph. Using a specific parabola with vertex (0, -5), learn key algebra concepts such as quadratic functions and vertex form. Suitable for students in Grades 9-11.

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