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

 Feb 12, 2021
 #1
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The line  will only intersect  the parabola once  at  the  vertex  

 

To find  the  y coordinate  of  the  vertex  we  have    ( 3)  /(2 (-2))  =  -3/4

 

To  find  the x coordinate  we  have

 

-2(-3/4)^2 - 3(-3/4)  +  5      =  49/8

 

This  is   the "k" we  need

 

So....the line is    x = 49/8

 

See the graph here  : https://www.desmos.com/calculator/av4pagctlb

 

 

cool cool cool 

 Feb 12, 2021
 #2
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Thanks so much!!!

Guest Feb 12, 2021

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