Answer
$y=\frac{1}{8}x^2 -\frac{3}{4}x +1$
Work Step by Step
$y$ = a$x^2$ + b$x$ + c
Substitute from the equation $(2,0), (4,0),$ and $(0,1)$
$0 = 2^2$a + $2$b +c
$0 = 4^2$a + $4$b +c
$1 = 0^2$a + $0$b +c
$0 = 4$a + $2$b +c
$0 = 16$a + $4$b +c
$1 = $ c
By simultaneous equation calculator
a $=\frac{1}{8}$
b $=-\frac{3}{4}$
c $=1$
Therefore, $y=\frac{1}{8}x^2 -\frac{3}{4}x +1$
