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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?

 Feb 14, 2021
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The parabola is a sideways parabola....to intersect at only one point ist must intersect at the vertex

 

-y^2 -3y - 5    = x

y^2 + 3y+5 =  -x

 

(y+1.5)^2 + 2.75 = -x

x = (-1)(y+1.5)^2 - 2.75

      the x point of the vertex is - 2.75        x =- 2.75

 Feb 14, 2021

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