Choice -12 is correct. The equation of a parabola in the xy-plane can be written in the form , where is a constant and is the vertex of the parabola. If is positive, the parabola will open upward, and if is negative, the parabola will open downward. Itâ€™s given that the parabola has vertex . Substituting for and for in the equation gives , which can be rewritten as , or . Distributing the factor of on the right-hand side of this equation yields . Therefore, the equation of the parabola, , can be written in the form , where , , and . Substituting for and for in the expression yields , or . Since the vertex of the parabola, , is below the x-axis, and itâ€™s given that the parabola intersects the x-axis at two points, the parabola must open upward. Therefore, the constant must have a positive value. Setting the expression equal to the value in choice D yields . Adding to both sides of this equation yields . Dividing both sides of this equation by yields , which is a positive value. Therefore, if the equation of the parabola is written in the form , where , , and are constants, the value of could be -12.

Choice -23 is incorrect. If the equation of a parabola with a vertex at is written in the form , where , , and are constants and , then the value of will be negative, which means the parabola will open downward, not upward, and will intersect the x-axis at zero points, not two points.

Choice -19 is incorrect. If the equation of a parabola with a vertex at is written in the form , where , , and are constants and , then the value of will be negative, which means the parabola will open downward, not upward, and will intersect the x-axis at zero points, not two points.

Choice -14 is incorrect. If the equation of a parabola with a vertex at is written in the form , where , , and are constants and , then the value of will be , which is inconsistent with the equation of a parabola.