Question

Seja f (x) = ax quadrado + bx + c sabendo que f(0) = 6 f( 1) = 2 e f (-2)= 20 Dtermine o valor de f (3/2)

Answer 1

$Se \ f(x)=ax^2+bx+c:\\\\ f(0)=6\\ f(0)=a.0^2+b.0+c\\ f(0)=c \implies \ c=6\\\\ f(1)=2\\ f(1)=a.1^2+b.1+6\\ f(1)=a+b+6\\ a+b+6=2\\ a+b=-4 \implies \ b=-4-a\\\\ f(-2)=20\\ f(-2)=a.(-2)^2+b.(-2)+6\\ f(-2)=4a-2b+6\\ 4a-2b+6=20\\ 4a-2b=20-6\\ 4a-2b=14\\ 2a-b=7\\\\ 2a-(-4-a)=7\\ 2a+4+a=7\\ 3a=7-4\\ 3a=3\\ a=1\\\\ b=-4-a\\ b=-4-1\\ b=-5$
$Agora \ f(x) \ fica:\\\\ f(x)=x^2-5x+6\\\\ f(\frac{3}{2})=(\frac{3}{2})^2-5(\frac{3}{2})+6\\\\ f(\frac{3}{2})=\frac{9}{4}-\frac{15}{2}+6\\\\ f(\frac{3}{2})=\frac{9-15.2+6.2}{4}\\\\ f(\frac{3}{2})=\frac{9-30+12}{4}\\\\ f(\frac{3}{2})=\frac{-9}{4}$