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The image you've uploaded contains a graph of a quadratic function along with some questions related to its properties. Here's how to solve it step-by-step:

### 1. **Vertex**
   - The vertex of the parabola is the highest or lowest point on the graph. From the graph, the vertex appears to be at \((2, 4)\).

### 2. **Axis of Symmetry**
   - The axis of symmetry is a vertical line that passes through the vertex. The equation for the axis of symmetry is \(x = 2\).

### 3. **Direction of Opening**
   - The parabola opens downwards because it is facing down, which means the leading coefficient of the quadratic function is negative.

### 4. **Y-intercept**
   - The y-intercept is the point where the graph crosses the y-axis. This happens when \(x = 0\). By looking at the graph, the y-intercept appears to be at \( (0, 0) \).

### 5. **Equation of the Quadratic Function**
   - Given the vertex \((2, 4)\) and knowing it opens downward, the general form of the equation is:
     \[
     y = -a(x - 2)^2 + 4
     \]
   - Using the y-intercept \((0, 0)\) to find \(a\):
     \[
     0 = -a(0 - 2)^2 + 4
     \]
     \[
     -4 = -4a \quad \Rightarrow \quad a = 1
     \]
   - Therefore, the equation is:
     \[
     y = -(x - 2)^2 + 4
     \]

Would you like to dive into more details or have any questions?

### Relative Questions:
1. How would the graph change if the parabola opened upwards?
2. What is the significance of the vertex in a quadratic function?
3. How do you determine the axis of symmetry from a quadratic equation?
4. Can the vertex form of a quadratic equation be converted to the standard form?
5. What is the effect of changing the value of \(a\) in the vertex form of a quadratic function?

### Tip:
Always check the direction of the parabola (whether it opens upwards or downwards) as it helps determine the sign of the leading coefficient in the quadratic equation.

Use the graph of a quadratic function to find the vertex, axis of symmetry, direction of opening, and y-intercept, then determine the equation of the quadratic function.

Step-by-step guide on how to find the vertex, axis of symmetry, direction of opening, and y-intercept of a quadratic function from its graph. Learn to determine the equation of the quadratic function using these properties. Suitable for students in Grades 8-10.

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