Fall 2024 The graph of a quadratic function is given.Determine the function's equation. 1)

To determine the equation of a quadratic function from its graph, we need to identify key features such as the vertex, axis of symmetry, and any points through which the graph passes. The general form of a quadratic function is: Alternatively, if we know the vertex \((h, k)\), we can use the vertex form: Let's go through the steps to find the equation:1. **Identify the Vertex**: The vertex form of a quadratic function is useful if we know the vertex. Suppose the vertex is at \((h, k)\).2. **Determine the Value of **: To find , we need another point on the graph. Let's say the graph passes through the point \((x_1, y_1)\).3. **Substitute the Values**: Substitute the vertex and the point into the vertex form to solve for .4. **Write the Equation**: Once is determined, write the full equation in vertex form or convert it to standard form if needed.### ExampleSuppose the graph has a vertex at \((2, 3)\) and passes through the point \((4, 7)\).1. **Vertex Form**: Start with the vertex form of the quadratic equation: 2. **Substitute the Point (4, 7)**: 3. **Solve for **: 4. **Write the Equation**: If you prefer the standard form, expand the vertex form: Thus, the equation of the quadratic function is: If you provide specific details about the graph, such as the vertex and another point, I can give you a more precise equation.