Parabola, determine the signs of the coefficients

Question

Consider the parabola y=ax²+bx+c. Determine the signs of the coefficients a and c if it is known that the vertex of the parabola has a negative y-coordinate, and the parabola never intersects the x-axis.

Answer 1

If the y-coordinate of the vertex is negative, the vertex is below the abscissa (x-axis).

"c" must be negative, and | c | > (b²/4a²).

If the parabola does not intersect the x-axis it must open downward. Therefore "a" must be negative.