The line x = k intersects the graph of the parabola x = -y^2 - 3y - 5 at exactly one point. What is k?
x = -y^2 - 3y - 5 is a 'sideways' parabola...for a line vertical line, x= k , to intersect at only ONE point it must intersect at the vertex....find the 'x' value of the vertex:
x = -y^2 - 3y - 5
x = -1(y^2 + 3) - 5
x = - (y+1.5)^2 + 2.25 -5
x = -(y+1.5)^2 - 2.75 (h,k) = ( -2.75, -1.5) k = - 2.75