To determine the equation of the quadratic function in standard form \( y = ax^2 + bx + c \), we need to identify three key points on the parabola: the vertex and two additional points, or the y-intercept and any other point.
1. Identify the Vertex:
- If you can see the vertex on the graph, note its coordinates. Let's say the vertex is at \( (h, k) \).
2. Identify another point:
- Look for another distinct point on the parabola. For example, if the parabola passes through \( (x_1, y_1) \).
3. Write the standard form equation:
- Use the vertex form of a quadratic equation, which is \( y = a(x - h)^2 + k \).
- Plug in the vertex coordinates and the coordinates of the other point to solve for \( a \).
4. Convert to standard form:
- Expand the vertex form to obtain the standard form \( y = ax^2 + bx + c \).
Since I don't have access to the image itself or specific points, I can't compute exact values. If you provide the coordinates of the vertex and another point, I can walk you through to find the equation.