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The image provided contains a mathematical problem involving a quadratic function and its graph, focusing on identifying the vertex form of the quadratic equation and solving related questions.

### Step-by-Step Solution

#### 1. Vertex Form of a Quadratic Function
The vertex form of a quadratic function is given by:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.

#### 2. Given Information and Interpretation
From the image:
- The quadratic function is graphed.
- The standard form of the quadratic equation is provided: \( y = x^2 + 2x - 3 \).

#### 3. Finding the Vertex
To convert \( y = x^2 + 2x - 3 \) to vertex form, we complete the square:
\[ y = x^2 + 2x - 3 \]
\[ y = (x^2 + 2x + 1) - 1 - 3 \]
\[ y = (x + 1)^2 - 4 \]

Thus, the vertex form is:
\[ y = (x + 1)^2 - 4 \]
and the vertex \((h, k)\) is \((-1, -4)\).

#### 4. Verifying with the Graph
Check the vertex \((-1, -4)\) on the graph provided in the image to confirm accuracy.

#### 5. Additional Problems in the Image
The image also shows a table and additional instructions to solve problems involving the quadratic equation. Let's address those problems sequentially.

### Solving the Questions

#### Question 1: What is the axis of symmetry?
The axis of symmetry for the quadratic function \( y = (x + 1)^2 - 4 \) is the vertical line passing through the vertex:
\[ x = -1 \]

#### Question 2: What is the minimum value of the function?
Since the parabola opens upwards (the coefficient of \((x+1)^2\) is positive), the minimum value of the function is at the vertex:
\[ y = -4 \]

#### Question 3: What are the x-intercepts of the function?
Set \( y = 0 \) in the standard form to find the x-intercepts:
\[ x^2 + 2x - 3 = 0 \]
Factorize the quadratic equation:
\[ (x + 3)(x - 1) = 0 \]
So, the x-intercepts are:
\[ x = -3 \text{ and } x = 1 \]

#### Question 4: Completing the square to find the vertex form
Already done above: \( y = (x + 1)^2 - 4 \)

#### Question 5: Drawing a table of values
Using the equation \( y = x^2 + 2x - 3 \), calculate and fill the table for selected x-values.

| x  | y          |
|----|------------|
| -3 | (-3)^2 + 2(-3) - 3 = 0 |
| -2 | (-2)^2 + 2(-2) - 3 = -3 |
| -1 | (-1)^2 + 2(-1) - 3 = -4 |
|  0 | 0^2 + 2(0) - 3 = -3 |
|  1 | 1^2 + 2(1) - 3 = 0 |

### Summary
- The vertex form is \( y = (x + 1)^2 - 4 \).
- Vertex: \((-1, -4)\).
- Axis of symmetry: \( x = -1 \).
- Minimum value: \( y = -4 \).
- X-intercepts: \( x = -3 \) and \( x = 1 \).

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

Here are some related questions for further practice:
1. How do you derive the standard form of a quadratic equation from the vertex form?
2. What are the steps to find the maximum value of a quadratic function that opens downwards?
3. How can you determine the direction of the parabola from the quadratic equation?
4. What is the significance of the discriminant in a quadratic equation?
5. How do you graph a quadratic function using its vertex and intercepts?

**Tip:** Always double-check your vertex and axis of symmetry calculations, as they are critical in graphing the quadratic function accurately.

What is the vertex form of the quadratic equation y = x^2 + 2x - 3, and solve related questions regarding axis of symmetry, minimum value, x-intercepts, and table of values?

Understand how to convert the quadratic equation y = x^2 + 2x - 3 to its vertex form and solve related problems, including finding the vertex, axis of symmetry, minimum value, and x-intercepts. Suitable for Grades 9-11.

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