一、试卷概述
2017年全国2卷数学试卷分为文科和理科两部分，涵盖了数学的基础知识和应用能力，包括选择题、填空题、解答题等题型。以下将针对该试卷的答案进行详细解析，帮助考生掌握解题技巧。
二、选择题解析
1. 选择题一
题目：若函数\(f(x) = ax^2 + bx + c\)在\(x=1\)时取得最小值，则\(a\)、\(b\)、\(c\)的关系是？
答案：\(a > 0\)，\(b^2 - 4ac \geq 0\)
解析：这是一个关于二次函数的问题。首先，由于函数在\(x=1\)时取得最小值，说明对称轴\(x=-\frac{b}{2a}=1\)，因此\(a > 0\)。其次，由于函数在\(x=1\)时取得最小值，所以函数的判别式\(Δ=b^2 - 4ac \geq 0\)。
2. 选择题二
题目：已知等差数列\(\{a_n\}\)的首项为\(a_1\)，公差为\(d\)，若\(a_5=10\)，\(a_{10}=20\)，则\(a_1\)的值为？
答案：\(a_1=2\)
解析：根据等差数列的通项公式\(a_n=a_1+(n-1)d\)，代入\(a_5=10\)和\(a_{10}=20\)，得到\(2a_1+4d=10\)和\(2a_1+9d=20\)。解这个方程组，得到\(a_1=2\)。
三、填空题解析
1. 填空题一
题目：若函数\(f(x) = \frac{x^2}{2} - x + 1\)的图像关于直线\(x=1\)对称，则$f(0)=______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________