Problem solving with quadratic functions.

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SUMMARY

The discussion centers on solving a quadratic function related to the planting of soybeans by an Illinois farmer, where the number of acres planted (q) is dependent on the selling price per bushel (p). The farmer will plant between 800 and 2000 acres based on price, with a linear relationship established between q and p. The correct formulation of the function is q = 0.003125p + 1999.96875, with the domain defined as 800 < q < 2000. The key takeaway is the importance of identifying independent and dependent variables in function formulation.

PREREQUISITES
  • Understanding of linear equations and their graphical representation.
  • Familiarity with the concepts of independent and dependent variables.
  • Basic knowledge of quadratic functions and their applications.
  • Ability to interpret word problems in mathematical terms.
NEXT STEPS
  • Study linear relationships and how to derive equations from word problems.
  • Learn about the graphical representation of functions using tools like Desmos or GeoGebra.
  • Explore the concept of domain and range in mathematical functions.
  • Practice solving real-world problems involving quadratic functions and their applications.
USEFUL FOR

Students studying algebra, educators teaching quadratic functions, and anyone interested in applying mathematical concepts to real-world agricultural scenarios.

davie08
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Homework Statement


okay I know understand that I should get a reasonable understanding about the questions I post before I post them sorry about before.

An Illinois farmer will plant from 800 to 2000 acres of soybeans. The number of acres q that he will plant depends on the selling price per bushel p that is being paid in April. Suppose that if p=$10, then all 2000 acres will be planted, but if p=$6.25, then only 800 acres will be planted.

a)Assuming p and q are linearly related, find q as a function of p, giving a suitable domain.


Homework Equations





The Attempt at a Solution



for some reason this question seems to work out to be the opposite of what I've been doing with my other word problems, here's what I tried.

(2000,10) and (800,6.25)


m=6.25-10/800-2000 = .003125

q-q1 = m(p-p1)

q-2000 = .003125(p-10)

q-2000 = .003125p - .03125

q= .003125p + 1999.96875 800<q<2000


so this is the wrong answer and to get the right answer I have to make p my x and q my y. Then for the domain you find what it is for price.

But I just saw a tutor and she has it on a formula sheet that x=q and p=y.
 
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davie08 said:
The number of acres q that he will plant depends on the selling price per bushel p

the clue here is "depends". Since q depends on p, p is the independent variable, which is always x.
 
okay thanks that makes sense.
 

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