### Graph of the Function \( f(x) = 0.25x^2 - 5 \) #### Description: The graph illustrates the quadratic function \( f(x) = 0.25x^2 - 5 \), which is a parabola opening upwards. The function is centered around the origin (0,0). #### Axes: - The x-axis ranges from -8 to 8. - The y-axis ranges from -6 to 6. #### Key Features: - **Parabola**: The curve shown is the parabola of the equation \( f(x) = 0.25x^2 - 5 \), opening upwards. The vertex of the parabola is located at a minimum point around \((0, -5)\). - **Tangent Line**: A blue tangent line is depicted touching the parabola. The tangent line indicates the slope at the point of tangency. The point where the tangent meets the curve is marked by a white dot. - **Slider and Options**: - **Slide Me!**: A slider allows for interaction with the graph, potentially changing the view or parameters. - **Show Labels**: This checkbox when activated would display labels on the graph. - **Show Grid**: This checkbox, if checked, would overlay a grid on the graph for better precision in viewing. - **Center (0,0)**: This point is marked to indicate the origin of the coordinate system. This visualization helps in understanding the behavior of quadratic functions and their tangent lines, providing a dynamic way to explore mathematical concepts.