determine the signs of the coefficents a and c if it is known that the vertex of the parabola has negative y coordinate and the parabola never intersects the x

Question

Consider the parabola y=ax^2+bx+c determine the signs of the coefficents a and c if it is known that the vertex of the parabola has negative y coordinate and the parabola never intersects the x

Answer 1

The vertex is below the x-axis and the parabola is negative. When the vertex is below the x-axis, the y coordinate of the vertex is negative. An example is

 

y = -x² - 1

 

The value of a is -1.  The value of c is -1.  Therefore, the signs of the coefficients of a and c are both negative.