The line x = k intersects the graph of the parabola x = -2y^2 - 3y + 5 - y^2 + 6 at exactly one point. What is k?
+128460 x = -2y^2 -3y + 5 - y^2 + 6 simplify as
x = -3y^2 - 3y + 11
This is a parabola that opens to the left.....the line will intercept the parabola at its vertex
The y coordinate of the vertex = - (-3) / ( 2 * -3) = 3/ -6 = -1/2
The x coordinate is -3(-1/2)^2 -3(-1/2) + 11 = -3/4 + 3/2 + 11 = 11+3/4 = 11.75
The equation of the line is x = the x cordinate of the vertex = 11.75
