Answer
One that opens upwards:
$y=x^2+\frac{7}{2}x+\frac{3}{2}$
One that opens downwards:
$y=-x^2-\frac{7}{2}x-\frac{3}{2}$
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.
$y=a[x-(-3)][x-(-\frac{1}{2})]=a(x^2+\frac{1}{2}x+3x+\frac{3}{2})=a(x^2+\frac{7}{2}x+\frac{3}{2})$
One that opens upwards ($a\gt0$).
$y=1(x^2+\frac{7}{2}x+\frac{3}{2})=x^2+\frac{7}{2}x+\frac{3}{2}$
One that opens downwards ($a\lt0$).
$y=-1(x^2+\frac{7}{2}x+\frac{3}{2})=-x^2-\frac{7}{2}x-\frac{3}{2}$
