小明根据学习函数的经验,对函数\(y={{x}^{4}}-5{{x}^{2}}+4\) 的图象与性质进行了探究.
下面是小明的探究过程,请补充完整:
\((1)\)自变量\(x\)的取值范围是全体实数,\(x\)与\(y\)的几组对应数值如下表:
\(x\) | \(…\) | \(-\dfrac{9}{4}\) | \(-\dfrac{11}{5}\) | \(-2\) | \(-\dfrac{3}{2}\) | \(-\dfrac{5}{4}\) | \(-1\) | \(-\dfrac{1}{2}\) | \(-\dfrac{1}{4}\) | \(0\) | \(\dfrac{1}{4}\) | \(\dfrac{1}{2}\) | \(1\) | \(\dfrac{5}{4}\) | \(\dfrac{3}{2}\) | \({\,\!}_{2}\) | \(\dfrac{11}{5}\) | \(\dfrac{9}{4}\) | \(…\) |
\(y\) | \(…\) | \(4.3\) | \(3.2\) | \(0\) | \(-2.2\) | \(-1.4\) | \(0\) | \(2.8\) | \(3.7\) | \(4\) | \(3.7\) | \(2.8\) | \(0\) | \(-1.4\) | \(-2.2\) | \(m\) | \(3.2\) | \(4.3\) | \(…\) |
其中\(m=\)________;
\((2)\)如图,在平面直角坐标系\(xOy\)中,描出了以上表中各组对应值为坐标的点,根据描出的点,画出该函数的图象;
\((3)\)观察函数图象,写出一条该函数的性质________________________;
\((4)\)进一步探究函数图象发现:
\(①\)方程\({{x}^{4}}-5{{x}^{2}}+4=0\)有_______个互不相等的实数根;
\(②\)有两个点\((x_{1},y_{1})\)和\((x_{2},y_{2})\)在此函数图象上,当\(x_{2} > x_{1} > 2\)时,比较\(y_{1}\)和\(y_{2}\)的大小关系为:
\(y_{1}\)__________\(y_{2}(\)填“\( > \)”、“\( < \)”或“\(=\)”\()\) ;
\(③\)若关于\(x\)的方程\({{x}^{4}}-5{{x}^{2}}+4=a\)有\(4\)个互不相等的实数根,则\(a\)的取值范围是___________.