Question

Espoque o grafico da funçao F(x)=x²+2x-3

Answer 1

$\boxed{\begin{array}{l}\rm f(x)= x^2+2x-3\\\rm a=1>0\longrightarrow concavidade\,para\,cima\\\underline{\sf intersecc_{\!\!,}\tilde ao\,com\,eixo\,x:}\\\rm f(x)=0\implies x^2+2x-3=0\\\rm\Delta=b^2-4ac\\\rm\Delta=2^2-4\cdot1\cdot(-3)\\\rm\Delta=4+12\\\rm\Delta=16\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-2\pm\sqrt{16}}{2\cdot1}\\\\\rm x=\dfrac{-2\pm4}{2}\begin{cases}\rm x_1=\dfrac{-2+4}{2}=\dfrac{2}{2}=1\\\\\rm x_2=\dfrac{-2-4}{2}=-\dfrac{6}{2}=-3\end{cases}\\\rm A(1,0)~~B(-3,0).\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\sf intersecc_{\!\!,}\tilde ao\,com\,eixo\,y:}\\\rm f(0)=0^2+2\cdot0-3\implies f(0)=-3\\\rm C(0,-3)\\\underline{\sf Coordenadas\,do\,v\acute ertice:}\\\rm x_V=-\dfrac{b}{2a}\\\\\rm x_V=-\dfrac{2}{2\cdot1}=-\dfrac{2}{2}=-1\\\\\rm y_V=-\dfrac{\Delta}{4a}\\\\\rm y_V=-\dfrac{16}{4\cdot1}=-\dfrac{16}{4}=-4\\\rm V(-1,-4)\\\boxed{\begin{array}{c|c}\rm x&\rm f(x)\\\rm1&\rm0\\\rm-3&\rm0\\\rm0&\rm-3\\\rm- 1&\rm-4\end{array}}\\\rm gr\acute afico\,est\acute a\,anexo.\end{array}}$