Suppose a quadratic equation has the form x^2 + x + c = 0. Show that the constant c must be less than 1/4 in order for the equation to have two real solutions.

For each expression use a property to write an equivalent expression.

Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?

Identify the converse of the following conditional: if a point is in the first quadrant, then its coordinates are positive. if the coordinates of a point are not positive, then the point is not in the first quadrant. if the coordinates of a point are positive, then the point is in the first quadrant. if a point is in the first quadrant, then its coordinates are positive. if a point is not in the first quadrant, then the coordinates of the point are not positive.