Answer
$a = \frac{4}{5}, b= -\frac{5}{3}, c=1$
Work Step by Step
$y=ax^{2} + bx +c$
$(-1,4)$
$a \times (-1)^{2} - b + c = 4$
$a - b + c = 4$
$(2,3)$
$a \times (2)^{2} + 2b + c = 3$
$4a + 2b + c = 3$
$(0,1)$
$c=1$
$a - b + c = 4$
$4a + 2b + c = 3$
$c=1$
$a - b + 1 =4$
$a-b=3$
$4a-4b = 12$ equation 1
$4a + 2b + 1 = 3 $
$4a + 2b = 2$ equation 2
(EQUATION 2) - (EQUATION 1)
$6b = -10$
$b=-\frac{10}{6} = -\frac{5}{3}$
$a-b=3$
$a=3+b=3-\frac{5}{3} = \frac{4}{3}$
$a = \frac{4}{3}, b =-\frac{5}{3}, c=1$
