Answer
One that opens upwards:
$y=x^2-3x-4$
One that opens downwards:
$y=-x^2+3x+4$
Work Step by Step
Use:
$y=a(x-x_1)(x-x_2)$, where $x_1$ and $x_2$ are the $x$ of the x-intercepts.
$y=a[x-(-1)](x-4)=a(x^2-4x+x-4)=a(x^2-3x-4)$
One that opens upwards ($a\gt0$).
$y=1(x^2-3x-4)=x^2-3x-4$
One that opens downwards ($a\lt0$).
$y=-1(x^2-3x-4)=-x^2+3x+4$
