Solving quadratic equations

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:

quadratic equation

Solving the Equation Symbolically

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:

 

 

quadratic equation

quadratic formula

quadratic formula

xapproximately equal13.4 or xapproximately equal-15.6

 Original Equation

Subtract 500000 from both sides

Use the quadratic formula with a = 2375,
b = 5134, c = -494,980

Simplifying


Simplifying

Since a year must be positive, x approximately equal13.4 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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