Question

y=-x²+3x alguém sabe o cálculo desse gráfico. Eu sei o gráfico, só não consigo fazer os cálculos ​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf Intersecc_{\!\!,}\tilde ao\,com\,o\,eixo\,x}\\\rm -x^2+3x=0\\\rm x\cdot(-x+3)=0\\\rm x=0\longrightarrow A(0,0)\\\rm -x+3=0\\\rm x=3\longrightarrow B(3,0)\\\underline{\sf Intersecc_{\!\!,}\tilde ao\,com\,eixo\,y}\\\rm y=0^2+3\cdot0=0\longrightarrow C(0,0)\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\sf Coordenadas\,do\,v\acute ertice}\\\rm\Delta=b^2-4ac\\\rm\Delta=3^2-4\cdot(-1)\cdot0\\\rm\Delta=9\\\rm x_V=-\dfrac{b}{2a}\\\\\rm x_V=-\dfrac{3}{2\cdot(-1)}=\dfrac{3}{2}\\\\\rm y_V=-\dfrac{\Delta}{4a}\\\\\rm y_V=-\dfrac{9}{4\cdot(-1)}\\\\\rm y_V=\dfrac{9}{4}\\\\\rm V( x_V,y_V)\\\\\rm V\bigg(\dfrac{3}{2},\dfrac{9}{4}\bigg)\end{array}}$

$\large\boxed{\begin{array}{l}\rm O\,gr\acute afico\,est\acute a\,anexo\end{array}}$