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For what constant $k$ is 1 the minimum value of the quadratic $3x^2 - 15x + k$ over all real values of $x$? ($x$ cannot be nonreal)

Guest Jan 18, 2018

Best Answer 

 #1
avatar+6943 
+1

the  x  coordinate of the minimum   =   -(-15) / [ 2(3) ]   =   15/6   =   5/2

 

the  y  coordinate of the minimum   =   3(5/2)^2 - 15(5/2) + k

 

1   =   3(5/2)^2 - 15(5/2) + k

 

1   =   3(25/4) - 75/2 + k

 

1   =   75/4 - 75/2 + k

 

1  =   -75/4 + k

 

1 + 75/4   =   k

 

79/4   =   k

hectictar  Jan 18, 2018
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1+0 Answers

 #1
avatar+6943 
+1
Best Answer

the  x  coordinate of the minimum   =   -(-15) / [ 2(3) ]   =   15/6   =   5/2

 

the  y  coordinate of the minimum   =   3(5/2)^2 - 15(5/2) + k

 

1   =   3(5/2)^2 - 15(5/2) + k

 

1   =   3(25/4) - 75/2 + k

 

1   =   75/4 - 75/2 + k

 

1  =   -75/4 + k

 

1 + 75/4   =   k

 

79/4   =   k

hectictar  Jan 18, 2018

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