The line \(x = k\) intersects the graph of the parabola \(x = -2y^2 - 3y + 5\) at exactly one point. What is k?
The line will be x = the x coordinate of the vertex = k
The y coordinate of the vertex = - (-3) / 2(-2) = 3 / -4 = -3/4
The x coordinate of the vertex = -2(-3/4)^2 - 3(-3/4) + 5 = -2(9/16) + 9/4 + 5 =
(-9/8) + 18/8 + 40/8 = 49/8
So....the line is
x = 49/8 = k
Here's a graph : https://www.desmos.com/calculator/yiurzdo46y