请把图中第5道题至第8道题，分别进行讲解---Here is the extracted content from the image: **Question 5:** **Question Stem:** 用配方法解方程 $x^2 - 4x + 1 = 0$ 时，结果正确的是 ( ) **Options:** A. $(x-2)^2 = 5$ B. $(x-2)^2 = 3$ C. $(x+2)^2 = 5$ D. $(x+2)^2 = 3$ **Mathematical Formulas:** $x^2 - 4x + 1 = 0$ $(x-2)^2 = 5$ $(x-2)^2 = 3$ $(x+2)^2 = 5$ $(x+2)^2 = 3$ --- **Question 6:** **Question Stem:** 二次函数 $y = ax^2 + bx + c$ 的 $x$ 与 $y$ 的部分对应值如下表: 则 $m$ 的值是 ( ) **Options:** A. 1 B. 2 C. 5 D. 10 **Mathematical Formulas:** $y = ax^2 + bx + c$ **Table:** | x | -1 | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---|---| | y | m | 2 | 1 | 2 | 5 | 10 | --- **Question 7:** **Question Stem:** 如图, 在 $\triangle ABC$ 中, $\angle BAC = 135^\circ$, 将 $\triangle ABC$ 绕点 $C$ 逆时针旋转得到 $\triangle DEC$, 点 $A,B$ 的对应点分别为 $D,E$, 连接 $AD$. 当点 $A,D,E$ 在同一条直线上时, 下列结论不正确的是 ( ) **Options:** A. $\triangle ABC \cong \triangle DEC$ B. $\angle ADC = 45^\circ$ C. $AD = \sqrt{2} AC$ D. $AE = AB + CD$ **Mathematical Formulas:** $\angle BAC = 135^\circ$ $AD = \sqrt{2} AC$ **Chart/Diagram Description:** Type: Geometric figure illustrating triangles and points. Main Elements: - Points: Labeled points A, B, C, D, E. - Shapes: Two triangles, $\triangle ABC$ and $\triangle CDE$. - Lines: Line segments AC, BC, AB, CD, CE, DE, AD, AE. - Angles: Angle $\angle BAC$ is indicated as $135^\circ$. Point C is the center of rotation. Points A, D, E lie on a straight line. - Relationships: $\triangle DEC$ is obtained by rotating $\triangle ABC$ counterclockwise around point C. Points A and D are corresponding points, B and E are corresponding points. AD is connected. A, D, E are collinear. --- **Question 8:** **Question Stem:** 如图, 已知关于 $x$ 的一元二次方程 $a(x-k)^2 - 1 = 0$ 的两根在数轴上对应的点分别在区域①和区域②, 区域均含端点, 则 $k$ 的值可能是 ( ) **Options:** A. -1 B. 0 C. 1 D. 2 **Mathematical Formulas:** $a(x-k)^2 - 1 = 0$ **Chart/Diagram Description:** Type: Number line. Main Elements: - Axis: Horizontal line with an arrow to the right, labeled with integers from -2 to 3. - Labels: Numbers -2, -1, 0, 1, 2, 3 are marked below the line. - Regions: Two regions are marked above the line. - Region ①: Indicated above the interval from -1 to 0, labeled with ①. This region includes the endpoints -1 and 0, represented by square brackets implicitly. - Region ②: Indicated above the interval from 2 to 3, labeled with ②. This region includes the endpoints 2 and 3, represented by square brackets implicitly. - Description: The two roots of the equation are located one in region ① and one in region ②. Regions include their endpoints.