The line x=k intersects the graph of the parabola x=-2y^2-3y+5 at exactly one point. What is k?

I tried that out on desmos and it said that it intersects it at 2 points. Plz tell me what I did wrong, or is the wording of this problem wrong? Thanks in advance!

Guest Nov 7, 2020

#1**0 **

This is a sideways parabola....for a vertical line to intersect at only one point , it must just touch the vertex (tangent at the vertex)

the y coordinate of the vertex is -b/2a - -3/(2*-2) = - 3/4

now sub this back into the equation to calculate the x coordinate of the vertex....this will be the 'k' value you are seeking....

Guest Nov 7, 2020