帮我讲一下，谢谢---**Header Information:**
思维训练营: 二次函数综合题线段及最值问题
一、线段及最值问题
基础衔接
**Question Stem:**
1. 如图，抛物线 y = - (1/2)x^2 + (3/2)x + 2 与x轴交于A, B两点，与y轴交于点C，点D是直线BC上方抛物线上任意一点，DF⊥x轴于点F，交直线BC于点E，过点D作DG⊥BC于点G。
**Sub-questions:**
(1)点A的坐标是__________, 点B的坐标为__________, 点C的坐标为__________, 直线BC的函数解析式为__________;
(2)线段AB的长为__________, 线段BC的长为__________;
**Other Relevant Text:**
义姐数学俱乐部
**Chart/Diagram Description:**
* **Type:** Cartesian coordinate plane with a parabola and a straight line.
* **Coordinate Axes:**
* A vertical Y-axis and a horizontal X-axis intersecting at the origin O.
* Arrows indicate the positive directions of the X and Y axes.
* **Parabola:**
* A downward-opening parabola (graph of y = - (1/2)x^2 + (3/2)x + 2).
* It intersects the X-axis at two points, A (on the negative x-axis side) and B (on the positive x-axis side).
* It intersects the Y-axis at point C (on the positive y-axis).
* **Line:**
* A straight line passes through points C and B.
* **Points:**
* A: X-intercept of the parabola.
* B: X-intercept of the parabola, also on line BC.
* C: Y-intercept of the parabola, also on line BC.
* O: Origin (0,0).
* D: A point on the parabola, located above the line BC.
* F: A point on the X-axis, directly below D.
* E: The intersection point of the vertical line segment DF and the line BC.
* G: A point on line BC, such that DG is perpendicular to BC.
* **Lines/Segments:**
* Line segment DF: A vertical line segment from point D to point F on the X-axis.
* Line segment DG: A line segment from point D to point G on line BC.
* **Angles:**
* A right angle symbol is shown at F, indicating DF ⊥ X-axis.
* A right angle symbol is shown at G, indicating DG ⊥ BC.
* **Relative Positions:**
* A is to the left of O.
* B is to the right of O.
* C is above O on the Y-axis.
* D is above line BC.
* F is on the X-axis below D.
* E is on line BC, between D and F (vertically).
* G is on line BC, where DG is perpendicular to BC.