1. **Stating the problem:** We want to find the equation of a parabola given its graph. 2. **General form of a parabola:** The standard form of a parabola that opens up or down is $$y = ax^2 + bx + c$$ where $a$, $b$, and $c$ are constants. 3. **Key features to identify:** To find $a$, $b$, and $c$, we need points from the graph such as the vertex, intercepts, or any points on the parabola. 4. **Using the vertex form:** If the vertex $(h, k)$ is known, the parabola can be written as $$y = a(x - h)^2 + k$$. 5. **Finding $a$:** Use another point $(x_1, y_1)$ on the parabola and substitute into the vertex form: $$y_1 = a(x_1 - h)^2 + k$$ Solve for $a$: $$a = \frac{y_1 - k}{(x_1 - h)^2}$$ 6. **Converting to standard form:** Expand the vertex form: $$y = a(x^2 - 2hx + h^2) + k = ax^2 - 2ahx + (ah^2 + k)$$ 7. **Summary:** - Identify vertex $(h,k)$ - Use another point to find $a$ - Write equation in vertex form and expand if needed This method allows you to find the equation of a parabola from its graph by using key points.