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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 can not be unreal

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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 can not be unreal

Guest Mar 4, 2017
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3x^2-15x+k

This is a parabola.... the x coordinate of the minimum value  = -b/2a

= 15/ (2(3) )  = 15/6  =

5/2

So...we have

1 = 3(5/2)^2 - 15(5/2) + k     simplify

1  = 3(25/4)  - 75/2  + k

1 = 75/4 - 75/2 + k

1 = -75/4  + k

4/4 + 75/4  = k   =  79/4

Here's a graph that confirms this : https://www.desmos.com/calculator/rzief47yod

CPhill  Mar 4, 2017

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