https://file.aiquickdraw.com/mathbot/file/1726667732339jmko1ptl.jpg

Let's go through the graphs and their properties one by one.

### For Graph 1 (Upward Parabola):

1. **X-intercepts**: 
   - The points where the graph crosses the x-axis. 
   - Looking at the graph, the x-intercepts are \( (-2, 0) \) and \( (2, 0) \).

2. **Zeroes**:
   - These are the x-values where the function equals zero, which are the same as the x-intercepts.
   - Zeroes: \( x = -2 \) and \( x = 2 \).

3. **Y-intercept**:
   - The point where the graph crosses the y-axis.
   - From the graph, the y-intercept is \( (0, -4) \).

4. **Vertex**:
   - The vertex is the turning point of the parabola.
   - From the graph, the vertex is at \( (0, -4) \).

5. **Axis of Symmetry**:
   - The vertical line that passes through the vertex.
   - The axis of symmetry is \( x = 0 \).

6. **Opening**:
   - The direction in which the parabola opens.
   - This parabola opens **upward**.

7. **Domain**:
   - The set of all possible x-values.
   - The domain is \( (-\infty, \infty) \).

8. **Range**:
   - The set of all possible y-values.
   - Since the vertex is the lowest point, the range is \( [-4, \infty) \).

9. **Minimum or Maximum Value**:
   - Since the parabola opens upwards, it has a minimum value at the vertex.
   - Minimum value: \( y = -4 \).

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### For Graph 2 (Downward Parabola):

1. **X-intercepts**:
   - The points where the graph crosses the x-axis.
   - From the graph, the x-intercepts are \( (-3, 0) \) and \( (3, 0) \).

2. **Zeroes**:
   - The x-values where the function equals zero, which are the same as the x-intercepts.
   - Zeroes: \( x = -3 \) and \( x = 3 \).

3. **Y-intercept**:
   - The point where the graph crosses the y-axis.
   - The y-intercept is \( (0, 9) \).

4. **Vertex**:
   - The vertex is the turning point of the parabola.
   - The vertex is \( (0, 9) \).

5. **Axis of Symmetry**:
   - The vertical line that passes through the vertex.
   - The axis of symmetry is \( x = 0 \).

6. **Opening**:
   - The direction in which the parabola opens.
   - This parabola opens **downward**.

7. **Domain**:
   - The set of all possible x-values.
   - The domain is \( (-\infty, \infty) \).

8. **Range**:
   - The set of all possible y-values.
   - Since the vertex is the highest point, the range is \( (-\infty, 9] \).

9. **Minimum or Maximum Value**:
   - Since the parabola opens downwards, it has a maximum value at the vertex.
   - Maximum value: \( y = 9 \).

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Would you like any further details on these graphs or their properties?

Here are some related questions to deepen your understanding:

1. How do you find the vertex algebraically from a quadratic equation?
2. What is the significance of the axis of symmetry in a parabola?
3. How can you determine the direction of the parabola's opening from its equation?
4. What role does the discriminant play in determining the number of x-intercepts?
5. Can the range of a parabola be \( (-\infty, \infty) \)? Why or why not?

**Tip**: The vertex form of a quadratic function is useful for easily identifying the vertex and the direction of opening. The general form is \( y = a(x-h)^2 + k \), where \( (h, k) \) is the vertex and \( a \) determines the direction and width of the parabola.

Describe each graph in terms of its properties.

Learn how to describe the properties of parabolas by identifying x-intercepts, y-intercepts, vertex, axis of symmetry, domain, range, and more. This detailed explanation covers upward and downward opening parabolas. Ideal for students in Grades 9-12 studying quadratic equations.

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