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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?

 Apr 16, 2020
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the only way the line can intersect this sideways parabola is if it is at the apex     - b/2a = 3/-4  = - .75

 

   Sub this value of y into the equation to calculate 'k'

 

 

 

Another way

  the discriminant must = 0 for only one intersection

k = -2y^2-3y+5

0 = -2y^2-3y+ ( 5-k)

    b^2 - 4ac   = 0

    (-3)^2 - 4(-2)(5-k) = 0

     9 +40 - 8k = 0

     49 = 8k

      k = 49/8 = 6 1/8    or   6.125

 Apr 16, 2020

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