SOLUTION: Find all values of p such that 2(x+4)(x-2p) has a minimum value of -18.

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Question 1026795: Find all values of p such that
2(x+4)(x-2p)
has a minimum value of -18.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The roots are x+4 and x-2p.

Zeros are x=-4 and x=2p.
The exact middle value between these zeros is %28-4%2B2p%29%2F2=p-2.

Minimum value for 2%28x%2B4%29%28x-2p%29=-18 needs x=p-2.
2%28p-2%2B4%29%28p-2-2p%29=-18
%28p%2B2%29%28-p-2%29=-9
%28p%2B2%29%28p%2B2%29=9
p%2B2=0%2B-+3
highlight%28p=-2%2B-+3%29

p=1 or p=-5.