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The line x = k intersects the graph of the parabola x = -2y^2 - 3y + 5 - y^2 + 6 at exactly one point. What is k?

 Jun 24, 2022
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x = -2y^2 -3y + 5 - y^2  + 6               simplify as

 

x =  -3y^2 - 3y + 11

 

This is a parabola that opens to  the left.....the line will intercept the parabola at  its vertex

 

The y coordinate of the vertex =  - (-3) / ( 2 * -3)  = 3/ -6  = -1/2

 

The x coordinate is     -3(-1/2)^2 -3(-1/2) + 11  =   -3/4 + 3/2  + 11  =  11+3/4 = 11.75

 

The equation of the line  is     x =  the x cordinate of the vertex =  11.75

 

 

cool cool cool

 Jun 24, 2022

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