Question

Find two quadratic functions, one that opens upward and one that opens downward, whose graphs have the given x-intercepts.

(-3, 0), (-1/2, 0)

Answer 1

Quadratic functions that have given x-intercepts x1 and x2 are given by the equation:
y=a(x-x1)(x-x2)

If a>0, the curve opens upwards, and if a<0, the curve opens downwards.
|a| can be any value ≠0 depending on the location of the vertex or any other point on the curve.