شاه کلید نکات
شاه کلید سوال
1 در هر یک از سهمی های زیر، رأس را مشخص و سپس آن را رسم کنید.
الف \(y = {\left( {x + 1} \right)^2} - 2\)
ب \(y = - 2{x^2} + 1\)
الف
\(\begin{array}{*{20}{l}}\begin{array}{l}y = {\left( {x + 1} \right)^2} - 2 \Rightarrow x + 1 = 0 \Rightarrow {x_0} = - 1\\\\ \Rightarrow {y_0} = {\left( { - 1 + 1} \right)^2} - 2 = - 2\end{array}\\\begin{array}{l}\\ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{x_0} = - 1}\\{{y_0} = - 2}\end{array}} \right. \Rightarrow \left( { - 1\,,\, - 2} \right)\end{array}\end{array}\)
نقطه رأس: (-1, -2)
\(\begin{array}{*{20}{l}}{{x_1} = - 2 \Rightarrow {y_1} = {{\left( { - 2 + 1} \right)}^2} - 2 = - 1}\\{ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{x_1} = - 2}\\{{y_1} = - 1}\end{array}} \right. \Rightarrow \left( { - 2\,,\, - 1} \right)}\\{{x_2} = 0 \Rightarrow {y_2} = {{\left( {0 + 1} \right)}^2} - 2 = - 1}\\{ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{x_2} = 0}\\{{y_2} = - 1}\end{array}} \right. \Rightarrow \left( {0\,,\, - 1} \right)}\end{array}\)
ب
\(\begin{array}{*{20}{l}}{y = - 2{x^2} + 1 \Rightarrow {x_0} = 0 \Rightarrow {y_0} = - 2{{\left( 0 \right)}^2} + 1 = 1}\\{ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{x_0} = 0}\\{{y_0} = 1}\end{array}} \right. \Rightarrow \left( {0\,,\,1} \right)}\end{array}\)
نقطه رأس: (0, 1)
\(\begin{array}{*{20}{l}}{{x_1} = - 1 \Rightarrow {y_1} = - 2{{\left( { - 1} \right)}^2} + 1 = - 1}\\{ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{x_1} = - 1}\\{{y_1} = - 1}\end{array}} \right. \Rightarrow \left( { - 1\,,\, - 1} \right)}\\{{x_2} = 1 \Rightarrow {y_2} = - 2{{\left( 1 \right)}^2} + 1 = - 1}\\{ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{x_2} = 1}\\{{y_2} = - 1}\end{array}} \right. \Rightarrow \left( {1\,,\, - 1} \right)}\end{array}\)
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