讲解这份试卷---**Question 6** * **Question Stem:** 已知二次函数 y=ax²+bx+c (a≠0) 与 x 轴的一个交点为 (4,0), 其对称轴为直线 x=1, 其部分图象如图所示, 有下列 5 个结论: ① abc < 0; ② b²-4ac < 0; ③ 9a + 3b + c = 0; ④ 8a + c = 0; ⑤ 若关于 x 的方程 ax²+bx+c = -1 有两个实数根 x₁, x₂, 且满足 x₁ < x₂, 则 x₁ < -2, x₂ > 4. 其中正确结论的个数为 ( ) * **Options:** A. 4 B. 3 C. 2 D. 1 * **Diagram Description:** * **Type:** Parabola graph on a Cartesian coordinate system. * **Coordinate Axes:** X-axis and Y-axis intersecting at the origin O. X-axis is labeled with points -2, O, 1, 4. Y-axis is labeled. * **Shape:** A downward-opening parabola (since a < 0 is suggested by the shape). * **Key Points/Lines:** * The parabola intersects the x-axis at (4,0). * A vertical dashed line at x=1 is shown, representing the axis of symmetry. * The vertex of the parabola is located on the axis of symmetry (x=1) and is above the x-axis. * **Annotations:** The parabola graph is shown. **Question 7** * **Question Stem:** 如图, 抛物线 y=a₁x² 与抛物线 y=a₂x²+bx 相交于点 P(-1,m), 过点 P 作 x 轴的平行线, 与两条抛物线分别交于点 M, N, 若点 M 是 PN 的中点, 则 $\frac{a₁}{a₂}$ 的值是 ( ) * **Options:** A. $\frac{1}{2}$ B. 2 C. $\frac{1}{3}$ D. 3 * **Diagram Description:** * **Type:** Graphs of two parabolas on a Cartesian coordinate system. * **Coordinate Axes:** X-axis and Y-axis intersecting at the origin O. * **Shapes:** Two upward-opening parabolas. * **Key Points/Lines:** * Both parabolas appear to pass through the origin O. * Point P is marked in the second quadrant, labeled P, with coordinates (-1, y). * A horizontal line passes through P. * This horizontal line intersects the two parabolas at points M and N. M is located to the right of P and N is located to the right of M on the horizontal line segment. The diagram indicates that M is the midpoint of the line segment PN. **Section Heading: 二、填空题 (Fill-in-the-blank question)** **Question 8** * **Question Stem:** 已知 Rt△ABC 的直角顶点 C 与原点 O 重合, 点 A, B 都落在抛物线 y=4x² 上, 则 AB 与