Question

suppose a parabola has a vertex in quadrant IV and a<0 in the equation y=ax^2+bx+c. how many real solutions will the equation ax^2+bx+c=0 have?

Answer 1

Given the vertex is in quadrat IV, it is below the y-axis.

Given a < 0, the parabola open downdards.

Those two facts together implies that the parabola does not touch the y-axis, meaning y is never 0, and the equation ax^2 + bx + c =0 does not have any real solutions.

Answer; None