Expert: Paul Klarreich - 9/22/2008

Question
how to answer this question:

In 2000, the average income (I)for a doctor aged(x)years could be modeled by I(x)= -297x^2 + 31,000x - 523,000 pesos. For what ages did the average income for a doctor exceed Php 280,000?

Answer
Questioner:   Migs
Category:  Advanced Math
Private:  No
 
Subject:  Quadratic functions
Question:  how to answer this question:

In 2000, the average income (I)for a doctor aged(x)years could be modeled by I(x)= -297x^2 + 31,000x - 523,000 pesos. For what ages did the average income for a doctor exceed Php 280,000?
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Hi, Migs,

This will involve some calculator stuff, which I leave to you, but here is what you will want to do:

A Q.F. has the form:  y = ax^2 + bx + c.
When a < 0, the parabola opens downward -- its vertex is on top.  Therefore, its positive part is between the intercepts ( i.e. the roots of the EQUATION  ax^2 + bx + c = 0).

SO:

1. Write  -297x^2 + 31,000x - 523,000 = 280,000

2. Rewrite: -297x^2 + 31,000x - 803,000 = 0

3. Use the quadratic formula to solve it.  Whatever you get for your roots,  x1 and x2, the answer is the interval between them.