Question

xác định parabol (p): y=x2 +bx +c đi qua M(2,5) có tung độ đỉnh bằng -4

Answer 1

\(\left\{{}\begin{matrix}4+2b+c=5\\\frac{4.1.c-b^2}{4.1}=-4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}c=1-2b\\c=\frac{b^2}{4}-4\end{matrix}\right.\)

\(\Rightarrow1-2b=\frac{b^2}{4}-4\)

\(\Leftrightarrow\frac{b^2}{4}+2b-5=0\Rightarrow\left[{}\begin{matrix}b=2\Rightarrow c=-3\\b=-10\Rightarrow c=21\end{matrix}\right.\)

Có 2 parabol thỏa mãn: \(\left[{}\begin{matrix}y=x^2+2x-3\\y=x^2-10x+21\end{matrix}\right.\)