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
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