Question

Escreva a lei que define a função quadrática representada pelo gráfico abaixo.

Answer 1

$\boxed{\begin{array}{l}\sf A(-3,0)~B(4,0)~C(0,-4)\\\sf f(x)=ax^2+bx+c\\\sf f(0)=a\cdot 0^2+b\cdot 0+c\\\sf c=-4\\\sf f(-3)=a\cdot(-3)^2+b\cdot(-3)+(-4)\\\sf 9a-3b-4=0\\\sf 9a-3b=4\\\sf f(4)=a\cdot 4^2+b\cdot4+(-4)\\\sf 16a+4b-4=0\div(4)\\\sf 4a+b-1=0\\\sf 4a+b=1\\\begin{cases}\sf9a-3b=4\\\sf 4a+b=1\cdot3\end{cases}\\\\+\underline{\begin{cases}\sf 9a-\diagdown\!\!\!\!\! 3b=4\\\sf 12a+\diagdown\!\!\!\!\!3b=3\end{cases}}\\\sf21a=7\\\sf a=\dfrac{7\div7}{21\div7}=\dfrac{1}{3}\\\\\sf4a+b=1\\\sf4\cdot\dfrac{1}{3}+b=1\cdot3\\\sf 4+3b=3\\\sf 3b=3-4\\\sf 3b=-1\\\sf b=-\dfrac{1}{3}\\\sf f(x)=\dfrac{1}{3}x^2-\dfrac{1}{3}x-4\end{array}}$