Question

Faça o gráfico da função quadrática: y = – x² + 2x + 8​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm intersecc_{\!\!,}\tilde ao~da~par\acute abola~com~o~eixo~x:}\\\sf -x^2+2x+8=0\\\sf s=-\dfrac{2}{-1}=2\\\sf p=\dfrac{c}{a}\\\sf p=\dfrac{8}{-1}=-8\\\sf x_1=4~e~x_2=-2\\\sf A(4,0)~B(-2,0)\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm intersecc_{\!\!,}\tilde ao~da~par\acute abola~com~o~eixo~y:}\\\sf y=0^2+2\cdot0+8=8\\\sf C(0,8)\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm C\acute alculo~das~coordenadas~do~v\acute ertice:}\\\sf \Delta=b^2-4ac\\\sf\Delta=2^2-4\cdot(-1)\cdot8\\\sf\Delta=4+32\\\sf\Delta=36\\\sf x_V=-\dfrac{b}{2a}\\\sf x_V=-\dfrac{\backslash\!\!\!2}{\backslash\!\!\!2\cdot(-1)}=1\\\sf y_V=-\dfrac{\Delta}{4a}\\\sf y_V=-\dfrac{36}{4\cdot(-1)}=\dfrac{36}{4}=9\\\sf V(1,9)\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm o~gr\acute afico~est\acute a~anexo}\end{array}}$