Asked by boe

By completing the square, determine the point in time when your model predicts Peter’s fortune will turn around. What is the lowest value that Peter’s investment will reach at this time?

my function was v(t)=25x^2-750x+10000

v(9)=25(9)^2-750(9)+10000=5275
Answered by Steve
the vertex of ax^2+bx+c is at x = -b/2a

In this case, that is 750/50 = 15, not 9.

v(15) = 4375
Answered by joey
v(t) = (5x-75)^2 + 4375
so the lowest value possible for v(t) is 4375 at x=15.
Answered by Reiny
It specified "completing the square", so

v(x) = 25x^2 - 750x + 10000 , you had v(t) but no t showed up in your function.

= 25(x^2 - 30x) + 10000
= 25(x^2 - 30x + 225 - 225) + 10000
= 25( (x-15)^2 - 225) + 10000
= 25(x-15)^2 - 5625+10000
= 25(x-15)^2 + 4375

lowest value is 4375 , when x = 15
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