The line x = k intersects the graph of the parabola x = -2y^2 - 8y + 5 at exactly one point. What is k?

Guest Jul 28, 2021

#1**+1 **

For a line x=k (a vertical line) to intersect a horizontal parabola at only one point, that point must be the vertex....do you know how to find the vertex?

ElectricPavlov Jul 28, 2021

#2**+1 **

-2 (y^{2} +4y) + 5

x = -2 (y+2)^{2 }+13

this is a sideways parabola of the form x = a(y-k)^{2} +h The vertex is 13,-2

so the line x = k = 13 will touch in only one point

ElectricPavlov
Jul 29, 2021