The Problem 
The quadratic function given by models the number of AIDS deaths from 1984 to 1994. Determine an equation whose solution is the year when the number of AIDS deaths might reach 500,000. Then solve the equation graphically and symbolically. 
The number 500,000 in this
problem represents the value of f(x).
So replacing f(x) with 500,000 gives us the following equation
to solve:

Solving symbolically means using the normal procedures of algebra to obtain a solution. In this case that means using the quadratic formula to solve this equation.
Quadratic Formula Given: Then:

x13.4 or x15.6 
Original
Equation
Subtract 500000 from both sides Use the quadratic formula
with a = 2375, Simplifying

Since a year must be positive, x 13.4 is the only possible solution.
Since x = 13 corresponds to 1984 + 13 = 1997, Thus, the number of AIDS deaths might reach 500,000 people in 1997.
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