+0  
 
0
44
1
avatar

For what constant k is -1 the minimum value of the quadratic 4x^2-12x+k+x^2+2x over all real values of x? x can not be unreal

 Jun 21, 2022
 #1
avatar+124509 
+1

Rearrange as

 

4x^2 +x^2  -12x + 2x  + k

 

5x^2  - 10x +  k 

 

The x coordinate of the  vertex of this  parabola   is     -(-10) / (2 *5)  =  10 / 10  = 1

 

So...we want

 

5(1)^2  - 10 (1)  +  k  =  - 1

 

5 -10 + k  =  -1

 

-5 + k = -1

 

k =  -1 + 5   =   4

 

 

cool cool cool

 Jun 21, 2022

15 Online Users

avatar