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

 Aug 6, 2021
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x = -y^2 - 3y - 5    is a 'sideways'  parabola...for a line vertical line, x= k ,  to intersect at only ONE point it must intersect at the vertex....find the 'x' value of the vertex:

x = -y^2 - 3y - 5

x = -1(y^2 + 3) - 5

x = - (y+1.5)^2 + 2.25 -5   

x = -(y+1.5)^2 - 2.75                        (h,k) = ( -2.75, -1.5)                      k = - 2.75

 Aug 7, 2021

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