(1)如图①,若抛物线图象与轴交于点,与轴交点.连接.
①求该抛物线所表示的二次函数表达式;
②若点是抛物线上一动点(与点不重合),过点作轴于点,与线段交于点.是否存在点使得点是线段的三等分点?若存在,请求出点的坐标;若不存在,请说明理由.
(2)如图②,直线与轴交于点,同时与抛物线交于点,以线段为边作菱形,使点落在轴的正半轴上,若该抛物线与线段没有交点,求的取值范围.
同类型试题
y = sin x, x∈R, y∈[–1,1],周期为2π,函数图像以 x = (π/2) + kπ 为对称轴
y = arcsin x, x∈[–1,1], y∈[–π/2,π/2]
sin x = 0 ←→ arcsin x = 0
sin x = 1/2 ←→ arcsin x = π/6
sin x = √2/2 ←→ arcsin x = π/4
sin x = 1 ←→ arcsin x = π/2
y = sin x, x∈R, y∈[–1,1],周期为2π,函数图像以 x = (π/2) + kπ 为对称轴
y = arcsin x, x∈[–1,1], y∈[–π/2,π/2]
sin x = 0 ←→ arcsin x = 0
sin x = 1/2 ←→ arcsin x = π/6
sin x = √2/2 ←→ arcsin x = π/4
sin x = 1 ←→ arcsin x = π/2