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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?

 Jul 16, 2019
 #1
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The line will be  x  =  the x coordinate of the vertex    =   k

 

The y coordinate of the vertex  =   - (-3) / 2(-2)  =  3 / -4  =  -3/4

 

The x coordinate of the vertex  =   -2(-3/4)^2 - 3(-3/4) + 5  =  -2(9/16) + 9/4 + 5  = 

 

(-9/8) + 18/8 + 40/8    =  49/8 

 

So....the line is

 

x  = 49/8  = k

 

Here's a graph :  https://www.desmos.com/calculator/yiurzdo46y

 

 

cool cool cool

 Jul 16, 2019

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