(1)求证:无论a取任何实数时,该方程总有实数根;
(2)若抛物线y=ax2+(3a+1)x+3的图象与x轴两个交点的横坐标均为整数,且a为正整数,求a值以及此时抛物线的顶点H的坐标;
(3)在(2)的条件下,直线y=﹣x+5与y轴交于点C,与直线OH交于点D.现将抛物线平移,保持顶点在直线OD上.若平移的抛物线与射线CD(含端点C)只有一个公共点,请直接写出它的顶点横坐标h的值或取值范围.
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