Question

Uma função f, do 2°grau, admite as raízes -1 e 2 e seu gráfico intercepta o eixo y no ponto (0;-4).
Expresse a lei dessa função no formato f(x) = ax2 + bx + c

Answer 1

$\large\boxed{\begin{array}{l}\rm f(x)=ax^2+bx+c\\\rm f(0)=a\cdot 0^2+b\cdot 0+c\\\rm c=-4\\\rm f(-1)=a\cdot(-1)^2+b\cdot(-1)-4\\\rm a-b-4=0\\\rm a-b=4\\\rm f(2)=a\cdot 2^2+b\cdot 2-4\\\rm 4a+2b-4=0\div2\\\rm 2a+b-2=0\\\rm 2a+b=2\end{array}}$

$\large\boxed{\begin{array}{l}+\underline{\begin{cases}\rm a-b=4\\\rm 2a+b=2\end{cases}}\\\rm 3a=6\\\rm a=\dfrac{6}{3}\\\\\rm a=2\\\rm a-b=4\\\rm b=a-4\\\rm b=2-4\\\rm b=-2\\\rm f(x)=2x^2-2x-4\end{array}}$