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# NEED HELP ASAP!

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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

#1
+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
Sort:

#1
+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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