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

 Jul 28, 2021
 #1
avatar+34313 
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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?

 Jul 28, 2021
 #2
avatar+34313 
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-2 (y2 +4y)    + 5

x = -2 (y+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

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