完成方块
如何将二次表达式的前两项写成两个平方之差?
- 看看这个二次表达式x2+bx+c
- 第一个两个术语可以写成the二平方之差使用下面的规则
- 通过展开右边来验证这是正确的
- 是
" class="Wirisformula" role="math" alt="X²+ 2x" style="vertical-align:-6px;height:23px;width:54px" loading="lazy">和x 2 + 2 x {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} " class="Wirisformula" role="math" alt="左括号(x + 1)右括号²- 1²" style="vertical-align:-6px;height:23px;width:89px" loading="lazy">?x + 1 2 - 1 2 {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}
- 是的:(x+ 1) (x+ 1) - 12=x2+ 2x+ 1 - 1 =x2+ 2x
- 是
- 这适用于负值b太
" class="Wirisformula" role="math" alt="X²- 20x" style="vertical-align:-6px;height:23px;width:63px" loading="lazy">可以写成x 2 - 20 x {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} " class="Wirisformula" role="math" alt="左括号(x - 10)右括号的平方减去(10)右括号的平方" style="vertical-align:-6px;height:23px;width:132px" loading="lazy">这是x - 10 2 - - 10 2 {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} " class="Wirisformula" role="math" alt="左括号x - 10右括号平方- 100" style="vertical-align:-6px;height:23px;width:109px" loading="lazy">x - 10 2 - 100 {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} - 一个负b结尾的符号不变吗
我如何完成这个方块?
- 完成正方形是否有一种方法可以将二次表达式重写为包含方括号的形式
- 完成上的方格x2+ 10x+ 9
- 用上面的规则替换前两项,x2+ 10x,(x+ 5)2- 52
- 加9:(x+ 5)2- 52+ 9
- 简化的数字:(x+ 5)2- 25+ 9
- 答:(x+ 5)2- 16
当前面有一个系数时,我如何完成这个平方x2术语?
- 你首先需要采取
" class="Wirisformula" role="math" alt="一个" style="vertical-align:-6px;height:22px;width:10px" loading="lazy">Out是的因子x2而且x条款只a {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="A x²+ b x + c等于A(左方括号x²+ b) / A x(右方括号+ c" style="vertical-align:-17px;height:47px;width:216px" loading="lazy">a x 2 + b x + c = a x 2 + b a x + c {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} - 使用方形括号为了避免后面和大括号混淆
- 然后在钻头上完成正方形内部方括号:
" class="Wirisformula" role="math" alt="X²+ b / ax" style="vertical-align:-17px;height:47px;width:63px" loading="lazy">x 2 + b a x {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} - 这给了
" class="Wirisformula" role="math" alt="左方括号,右括号x + p右括号平方减去p平方,右方括号加上c" style="vertical-align:-6px;height:23px;width:140px" loading="lazy">a x + p 2 - p 2 + c {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} - 在哪里p是一半
" class="Wirisformula" role="math" alt="B / a" style="vertical-align:-17px;height:47px;width:19px" loading="lazy">b a {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}
- 在哪里p是一半
- 这给了
- 最后将这个表达式乘以一个在方括号外,并添加c
" class="Wirisformula" role="math" alt="A,开括号x + p,闭括号²- A, p²+ c" style="vertical-align:-6px;height:23px;width:134px" loading="lazy">a x + p 2 - a p 2 + c {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} - 这看起来比实际要复杂得多!
- 通常你会被要求在表格中给出你的最终答案
" class="Wirisformula" role="math" alt="A,开括号x + p,闭括号²+ q" style="vertical-align:-6px;height:23px;width:93px" loading="lazy">a x + p 2 + q {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}
- 通常你会被要求在表格中给出你的最终答案
- 对于二次方程
" class="Wirisformula" role="math" alt="- x²+ bx + c" style="vertical-align:-6px;height:23px;width:93px" loading="lazy">,做上面的用一个= 1- x 2 + b x + c {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}
我如何通过完成正方形来找到转折点?
- 完成这个正方形可以帮助我们找到把点在二次图上
- 如果
" class="Wirisformula" role="math" alt="Y =开括号x + p闭括号²+ q" style="vertical-align:-6px;height:23px;width:111px" loading="lazy">那么转折点在y = x + p 2 + q {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} " class="Wirisformula" role="math" alt="开括号(- p, q)闭括号" style="vertical-align:-6px;height:22px;width:51px" loading="lazy">- p , q {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} - 注意这个负号x协调
- 这链接到图的转换(翻译
" class="Wirisformula" role="math" alt="Y = x²" style="vertical-align:-6px;height:23px;width:45px" loading="lazy">通过p在左边问)y = x 2 {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}
- 如果
" class="Wirisformula" role="math" alt="Y = a,开括号x + p,闭括号²+ q" style="vertical-align:-6px;height:23px;width:120px" loading="lazy">那么转折点仍然在y = a x + p 2 + q {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} " class="Wirisformula" role="math" alt="开括号(- p, q)闭括号" style="vertical-align:-6px;height:22px;width:51px" loading="lazy">- p , q {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} - 它在最小值处,如果一个> 0
- 它在最大值点,如果一个< 0
- 如果
- 它也可以帮助你创建方程在给定拐点的情况下
- 它也可以用来证明和/或显示结果使用任何“平方项”,即括号(x±p)2,总是大于或等于0
- 一个数的平方不可能得到负数
考试技巧
- 要知道你是否正确地完成了这个方格,展开你的答案来检查一下。
工作的例子
求+6的一半(记作p)
只把前两项分解成-2
使用方形支架
完成上的方格x2- 4x在括号内(填入表格(x+p)2-p2在哪里p是-4的一半)
化简括号内的数字
(2)2是4
将-3乘以方括号内的所有项
简化数字
这就是这个形式一个(x+p)2+问在哪里一个= 3,p= -2 and问= 36