Question

Write an equation for this parabola. The vertex is ( 1, 3)

Answer 1

$a(x - 4)(x + 2) = \\ a {x}^{2} - 2ax - 8a$
so put x=1 solve
$a - 2a - 8a = 3 > > > - 9a = 3 \\ a = \frac{ - 1}{3}$
then
$\frac{ - 1}{3} {x}^{2} + \frac{2}{3} + \frac{8}{3}$