The line $x = k$ intersects the graph of the parabola $x = -2y^2 - 3y + 5$ at exactly one point. What is $k$? Thanks!!!
The line will only intersect the parabola once at the vertex
To find the y coordinate of the vertex we have ( 3) /(2 (-2)) = -3/4
To find the x coordinate we have
-2(-3/4)^2 - 3(-3/4) + 5 = 49/8
This is the "k" we need
So....the line is x = 49/8
See the graph here : https://www.desmos.com/calculator/av4pagctlb