Question

a reta f(x)= -x corta a parábola f(x)= -2x^2 -2x + 3nos pontos: (A) (0,0) e (1,-1 ) (B) (1,-1) e (-3/2) (c) (-3/2) e (0,0) (D) (0,-1) e (0, -3/2)

Answer 1

Basta igualar:

$-x=-2x^2 -2x + 3\\ \\ 2x^2+x-3=0\\ \\ \Delta=1^2-4.2.(-3)\\ \\ \Delta=1+24\\ \\ \Delta=25\\ \\ x=\frac{-1\pm\sqrt{25}}{4}=\frac{-1\pm5}{4}\\ \\ x_1=-\frac{6}{4}=-\frac{3}{2}\\ \\ x_2=\frac{4}{4}=1$

$Se \ x=-\frac{3}{2} \Rightarrow y = \frac{3}{2} \ \ P_1=\left(-\frac{3}{2};\frac{3}{2}\right) \\ \\ Se \ x=1 \Rightarrow y=-1 \ \ P_2=(1;-1)$