SOLUTION: Function. V(t)=-3t^2+140t+824 models the numbers (in thousands), V(t), of murders committed in a certain state in the United states t years after 1960. Let t=0 represent 1960, t=1

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Question 1057852: Function. V(t)=-3t^2+140t+824 models the numbers (in thousands), V(t), of murders committed in a certain state in the United states t years after 1960. Let t=0 represent 1960, t=1 represent 1961, and so.
a. Determine the year in which the most violent crimes were committed. b. Approximately how many violent crimes were committed during this year? c. Using a graphing calculator, graph V(t). Were the number of violent crimes increasing or decreasing during the years 2000 to 2005?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28400%2C400%2C-10%2C40%2C-10%2C3000%2C-3x%5E2%2B140x%2B824%29

y=-3%28x%5E2-%28140%2F3%29x-824%2F3%29
y=-3%28x%5E2-%28140%2F3%29x%2B%28140%2F6%29%5E2-824%2F3-140%2F6%29------completing-the-square
y=-3%28%28x-140%2F6%29%5E2-%282%2A824-140%29%2F6%29
y=-3%28x-140%2F6%29%5E2%2B%282%2A824-140%29%2F2
y=-3%28x-140%2F6%29%5E2%2B%281508%29%2F2
y=-3%28x-70%2F3%29%5E2%2B754

If done well, this means t=70%2F3=23%2Aapproximately, year about 1983, when the maximum about 750 thousand occurred.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Function. V(t)=-3t^2+140t+824 models the numbers (in thousands), V(t), of murders committed in a certain state in the United states t years after 1960. Let t=0 represent 1960, t=1 represent 1961, and so.
a. Determine the year in which the most violent crimes were committed. b. Approximately how many violent crimes were committed during this year? c. Using a graphing calculator, graph V(t). Were the number of violent crimes increasing or decreasing during the years 2000 to 2005?
Maximum number of murders occurred when 

Substitute 70%2F3 for t in the equation to get the MAXIMUM number of murders in that year (1983). This should give you approximately 2,457.333333, or about 2,457,333 violent crimes/murders. 

This is EXTREMELY high, but that's what the results "say."