Form Quadratics from Word Problems
Translate story problems into quadratic equations and enter the coefficients in standard form.
Ch. 4 Quadratic Equations 4.2 Quadratic Equations Medium
Instructions
- Read the generated problem carefully and choose a variable x to represent the unknown (first person's initial amount).
- Form the expression for the other person's initial amount using S and x, then apply the changes described (lost/gained, etc.).
- Translate the relation into an equation, expand to standard quadratic form, and enter coefficients.
- Work through the guided steps. Use visualization to confirm intermediate results and roots.
Problem
Generating problem...
Progress 0/5 steps completed
Step 1 — Choose variable & express other person's amount
If x = first person's original amount, express the other person's
original amount in terms of x.
Enter an expression for the other person's original amount using x
and the total
If the first person has x marbles and the total is given, what
expression represents the second person's amount?
Step 2 — Apply the change (lost/gained)
Enter the expressions for the two new amounts after the loss/gain.
Enter the expression for the first person's amount after losing
marbles
Enter the expression for the second person's amount after losing
marbles
Both people lost the same number of marbles. Subtract this amount
from their original expressions.
Step 3 — Translate to equation
Write the relation from the story as an equation (e.g. (x-5)*(40-x)
= 124).
Enter the equation showing that the product of their new amounts
equals the given value
The product of their new amounts (from Step 2) equals the given
product value in the problem.
Step 4 — Expand and enter coefficients
Expand to standard form ax^2 + bx + c = 0 and enter a, b, c below.
Enter the coefficient of x squared in the standard form
x^2 +
Enter the coefficient of x in the standard form
x +
Enter the constant term in the standard form
= 0
Expand the equation from Step 3 and move all terms to one side to
get ax² + bx + c = 0 form.
Step 5 — Solve & interpret
Use the quadratic formula or factor to find roots. Enter the two
roots (order doesn't matter).
Enter the first solution of the quadratic equation
Enter the second solution of the quadratic equation
Use the quadratic formula or factoring to solve ax² + bx + c = 0.
These represent the original amounts.
Concept Mastery
Variable Expressions
Algebraic Changes
Equation Formation
Quadratic Solving
Visualization (GeoGebra)
Roots and step visuals will appear as you progress.
Why This Matters
This problem demonstrates how quadratic equations model real-world scenarios involving:
- Resource distribution and sharing problems
- Game theory and competitive scenarios
- Economic modeling of losses and gains
- Optimization problems in business contexts
Learning Connection
This activity builds problem-solving skills by connecting algebraic
manipulation with word problems, essential for real-world
mathematical modeling.
Challenge Level
Select problem difficulty level
Choose your challenge level before generating a new problem.