1. **Problem Statement:** Match the descriptions of the parabolas to their graphs and estimate the roots from the graphs. 2. **Understanding Roots of Quadratic Functions:** A quadratic function is generally written as $$y = ax^2 + bx + c$$. The roots (or zeros) are the values of $x$ where $y=0$. 3. **Key Rules:** - If the parabola touches the x-axis at exactly one point, it has a repeated root (also called a double root). - If the parabola crosses the x-axis at two points, it has two distinct roots. - If the parabola does not cross the x-axis, it has no real roots. 4. **Graph 1 Analysis:** - Parabola opens upwards. - Vertex is around $(1,0)$. - Crosses x-axis at $x \approx 1$ with a repeated root. 5. **Graph 2 Analysis:** - Parabola opens upwards. - Vertex is below the x-axis. - Crosses x-axis at two points: $x \approx -2$ and $x \approx 3$. 6. **Graph 3 Analysis:** - Parabola opens upwards. - Vertex is above the x-axis. - Does not cross the x-axis, so no roots. **Final answers:** - Repeated roots: $x = 1$ - Two roots: $x = -2$ and $x = 3$ - No roots: none This matches the descriptions given for each graph.