Đáp án:
\(y = - {x^2} + 2\)
Giải thích các bước giải:
\(\begin{array}{l}
Do:f\left( 1 \right) = 1\\
\to a + b + c = 1 \to a = 1 - b - c\\
f\left( { - 1} \right) = 1\\
\to a - b + c = 1\\
\to 1 - b - c - b + c = 1\\
\to - 2b = 0\\
\to b = 0\\
Do:\max f\left( x \right) = 2\\
\to \dfrac{{ - {b^2} + 4ac}}{{4a}} = 2\\
\to - {b^2} + 4ac = 8a\\
Thay:b = 0\\
\to 4ac = 8a\\
Thay:a = 1 - b - c = 1 - c\\
\to 4.\left( {1 - c} \right).c = 8\left( {1 - c} \right)\\
\to 4c - 4{c^2} = 8 - 8c\\
\to \left[ \begin{array}{l}
c = 2\\
c = 1
\end{array} \right. \to \left[ \begin{array}{l}
a = - 1\\
a = 0\left( l \right)
\end{array} \right.\\
\to y = - {x^2} + 2
\end{array}\)
