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在二次函数中有一类问题,可以利用平行于y轴的直线被二次函数与一次函数所截线段长度来求解的问题.在求线段最值,三角形,四边形的面积最值,线段与线段的数量关系等方面有着广泛的运用.例1(2012年株洲中考题)如图1,一次函数y=-12x+2分别交y轴、x轴于A、B两点,抛物线y=-x2+bx+c过A、B两点.(1)求这个抛物线的解析式;(2)作垂直x轴的直线x=t,在第一象限交直线AB于点M,交这个抛物线于点N.求当t取何值时,MN有最大值?最大值是多少?
There is a class of problems in the quadratic function, you can use the parallel to the y-axis is quadratic function and the linear function of the length of the section length to solve the problem. Find the line value, triangle, quadrilateral area value, Example 1 (Zhuzhou test in 2012) as shown in Figure 1, the first-order function y = -12x +2 respectively pay the y-axis, x-axis at A, B two points, the parabola y = -x2 + bx + c over A and B. (1) Find the parabola’s analytical expression. (2) Make a straight line x = t perpendicular to the x-axis. N. What is the value of t when MN, MN has a maximum? What is the maximum?