Question

Construa o grafico da função quadratica,determine os zeros ou raizes da função e o vertice da parabola:

a) f(x)= -x²+2x+8

b) f(x)= x²-2x-3

c)f(x)= x²-3x+3

Answer 1

a) multiplica por (-1) 

-x²+2x+8(-1) = x²-2x-8
$x= \frac{-(-2) +/- \sqrt{ (-2)^{2} -4.1.(-8)} }{2.1}$

$x= \frac{-2 +/- \sqrt{4+32} }{2}$

$x= \frac{ -2 +/-\sqrt{36}}{2}$

$x= \frac{-2+/- 6}{2}$

$x'= \frac{4}{2} = 2$

$x" = \frac{-2-6}{2} = \frac{-8}{2} = -4$

b) $x= \frac{(-2) +/- \sqrt{(-2^{2}) - 4.1.(-3)} }{2}$

$x= \frac{-2 +/- \sqrt{4}+12 }{2}$

$x= \frac{-2 +/- \sqrt{16} }{2}$

$x= \frac{-2+/- \sqrt{16} }{2}$

$x= \frac{-2+/-4}{2}$

$x'= \frac{-2-4}{2} = \frac{-6}{2} = -3$

$x"= \frac{-2+4}{2} = \frac{2}{2} = 1$

c) $x= \frac{(-3) +/- \sqrt{(-3)^{2} -4.1.3 } }{2}$

$x= \frac{-3 +/- \sqrt{9-12} }{2}$

$x= \frac{-3 +/- \sqrt{3} }{2}$