Question

04) sendo f(0)=x ao quadrado -6x+5,determine : a) f(0) b) f(-1/2) c) x tal que f (x) =0 d) x tal que f (x)=5 05) determine os valores de m e p para que os pontos (0,0) e (1,-9) pertençam ao grafico de y=(x-2)ao quadrado - p me ajudem por favooor

Answer 1

$Fun\c{c}\~ao:\\\\ f_{(x)}=x^2-6x+5\\\\\\ a)\ Para\ x =0:\\\\ f_{(0)}=(0)^2-6(0)+5\\\\ f_{(0)}=0-0+5\\\\ \boxed{f_{(0)}=5}\\\\\\ b)\ Para\ x=-\frac{1}{2}:\\\\ f_{(-\frac{1}{2})}=(-\frac{1}{2})^2-6(-\frac{1}{2})+5\\\\ f_{(-\frac{1}{2})}=\frac{1}{4}+3+5\\\\ f_{(-\frac{1}{2})}=\frac{1}{4}+8\\\\ \boxed{f_{(-\frac{1}{2})}=\frac{33}{4}}$


$c)\ Para\ f_{(x)}=0:\\\\ 0=x^2-6x+5\\\\ Resolvendo\ Bh\'askara:\\\\ x=\dfrac{-b\pm\sqrt{b^2-4.a.c}}{2.a}\\\\ x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4.(1).(5)}}{2.(1)}\\\\ x=\dfrac{6\pm\sqrt{36-20}}{2}\\\\ x=\dfrac{6\pm\sqrt{16}}{2}\\\\ x=\dfrac{6\pm4}{2}\\\\ x=3\pm2\\\\ \boxed{x'=3+2=5}\\\\ \boxed{x''=3-2=1}$


Espero ter ajudado.
Bons estudos!