1. **State the problem:** We have four equations and four graphs labeled i, ii, iii, and iv. We need to match each equation to its corresponding graph. 2. **List the equations:** (a) $y^2 = x$ (b) $x^2 = 4y$ (c) $x^2 = -\frac{1}{5} y$ (d) $y^2 = -10x$ 3. **Analyze each equation:** - Equation (a) $y^2 = x$ is a horizontal parabola opening to the right because $y^2$ is positive and equals $x$. - Equation (d) $y^2 = -10x$ is a horizontal parabola opening to the left because $y^2$ equals a negative multiple of $x$. - Equation (b) $x^2 = 4y$ is a vertical parabola opening upward because $x^2$ equals a positive multiple of $y$. - Equation (c) $x^2 = -\frac{1}{5} y$ is a vertical parabola opening downward because $x^2$ equals a negative multiple of $y$. 4. **Match with graphs:** - Graph i (top-left) shows a horizontal parabola opening right and left, so it matches equations with $y^2$ terms: (a) and (d). - Graph ii (top-right) shows a vertical parabola opening downward, matching (c). - Graph iii (bottom-left) shows a vertical parabola opening upward, matching (b). - Graph iv (bottom-right) shows a vertical parabola opening downward, but since (c) is already matched to ii, iv must be (d). 5. **Final matching:** - i: (a) $y^2 = x$ - ii: (d) $y^2 = -10x$ - iii: (b) $x^2 = 4y$ - iv: (c) $x^2 = -\frac{1}{5} y$ This matches the orientation and direction of each parabola with the given graphs.