https://file.aiquickdraw.com/mathbot/file/1728098477255beuo9euo.jpg

Let's analyze the graph and solve the problems based on the quadratic equation provided.

### Step-by-step analysis of the graph:

1. **Identifying the vertex**: 
   From the graph, we can see the parabola opens upwards, and the vertex is the lowest point. The x-coordinate of the vertex is at \(x = -3\) (given), and the y-coordinate looks to be at \(-4\). Therefore, the vertex is:
   \[
   (-3, -4)
   \]

2. **Identifying the y-intercept**:
   The y-intercept occurs where the parabola crosses the y-axis (i.e., where \(x = 0\)). From the graph, this happens at \((0, 2)\).

3. **Identifying the x-intercepts**:
   The x-intercepts occur where the parabola crosses the x-axis (i.e., where \(y = 0\)). From the graph, the x-intercepts appear to be at \(x = -5\) and \(x = -1\), so the intercepts are:
   \[
   (-5, 0) \quad \text{and} \quad (-1, 0)
   \]

4. **Equation of the axis of symmetry**:
   The axis of symmetry for a parabola passes through the vertex and is a vertical line. Since the x-coordinate of the vertex is \(-3\), the equation of the axis of symmetry is:
   \[
   x = -3
   \]

### Summary:
- Vertex: \((-3, -4)\)
- Y-intercept: \((0, 2)\)
- X-intercepts: \((-5, 0)\) and \((-1, 0)\)
- Axis of symmetry: \(x = -3\)

Would you like more details or have any questions on any part?

### Related questions:
1. How do you determine the vertex of a parabola algebraically?
2. How can you derive the quadratic equation from the vertex and intercepts?
3. What is the significance of the axis of symmetry in a quadratic function?
4. How do you calculate the y-intercept of a parabola from its equation?
5. What are the steps to find the x-intercepts using the quadratic formula?

**Tip**: For a quadratic equation in vertex form, \(y = a(x - h)^2 + k\), the vertex is \((h, k)\), and the axis of symmetry is \(x = h\).

Identify the vertex, y-intercept, x-intercepts, and equation of symmetry from the quadratic graph.

Analyze a quadratic graph to identify the vertex at (-3, -4), the y-intercept at (0, 2), and the x-intercepts at (-5, 0) and (-1, 0). Learn how to write the equation for the axis of symmetry: x = -3.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation