我这个题目不会，请解题---**Text Extraction:** 如图 1-1-3, 在平面直角坐标系中, 抛物线 $y = \frac{\sqrt{3}}{3}x^2 - \frac{2\sqrt{3}}{3}x - \sqrt{3}$ 与 $x$ 轴交于 $A$、 $B$ 两点 (点 $A$ 在点 $B$ 的左侧), 与 $y$ 轴交于点 $C$, 对称轴与 $x$ 轴交于点 $D$, 点 $E (4, n)$ 在抛物线上. (1) 直线 $AE$ 的解析式为 __________ ; (2) 点 $G$ 是线段 $CE$ 的中点, 将抛物线 $y = \frac{\sqrt{3}}{3}x^2 - \frac{2\sqrt{3}}{3}x - \sqrt{3}$ 沿 $x$ 轴正方向平移得到新抛物线 $y'$, 经过点 $D$, $y'$ 的顶点为点 $F$. 在新抛物线 $y'$ 的对称轴上, 是否存在一点 $Q$, 使得 $\triangle FGQ$ 为等腰三角形? 若存在, 直接写出点 $Q$ 的坐标; 若不存在, 请说明理由. 图 1-1-3 **Chart/Diagram Description:** * **Type:** Coordinate plane with a parabola and line segments. * **Coordinate Axes:** Horizontal x-axis and vertical y-axis intersecting at the origin O. Axes are labeled 'x' and 'y'. * **Parabola:** A parabola opening upwards, intersecting the x-axis at points A and B (A is to the left of B), and the y-axis at point C. The vertex of the parabola is below the x-axis. * **Points:** * A and B are on the x-axis where the parabola intersects. * C is on the y-axis where the parabola intersects. * D is on the x-axis, the intersection of the parabola's axis of symmetry and the x-axis. * E is a point on the parabola in the first quadrant. * O is the origin (intersection of x and y axes). * **Lines/Segments:** * The curve of the parabola. * A straight line segment connecting A and E. * A straight line segment connecting C and E. * A vertical dashed line representing the axis of symmetry of the parabola, passing through D. * **Labels:** Points A, O, C, D, B, E are labeled. The figure is titled "图 1-1-3".