Quadratic Algebra Word Problem Game

Quadratic Algebra Word Problem Quiz/Game
This game focuses on solving word problems involving Quadratics. Quadratic problems including a wide range of quadratic applications: Geometry (Area/Perimeter), Number Theory (Consecutive Integers), Physics (Projectiles), Business (Revenue), and Pythagorean Word Problems. Scroll down the page for a more detailed explanation.

 

 

How to Play the Quadratic Algebra Explorer Game

1. Look at the Problem: Read the problem carefully. Solve it and select one of the answers.
   
2. Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green. A hint will be given to help you find the correct answer.
   
3. Get a New Problem: Click “Next Question” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
4. Finish Game When you have completed 10 questions, your final score will be displayed.
    
   

How to Solve Quadratic Algebra Word Problems
Solving quadratic word problems is about translating a real-world story into a standard mathematical format. Most problems follow a predictable pattern: they describe a relationship between two variables that, when multiplied, create a squared term (x²).

Identify the Scenario Type
Most quadratic problems fall into one of three “templates.”
Recognizing the template tells you which formula to use:

Area Problems:
Usually involving rectangles (Area = Length × Width).
Example: “The length is 3 more than the width, and the area is 40.” → w(w+3) = 40.

Projectile Motion:
Dealing with objects thrown in the air. These usually provide a height (h) and time (t) equation.
Example: h = -16t² + v₀t + h₀.

Consecutive Integers:
Finding numbers in a sequence.
Example: “The product of two consecutive even integers is 48.” → x(x+2) = 48.

Set Up the Standard Form
To solve any quadratic, you must first get it into the Standard Form:
ax² + bx + c = 0
If you have an equation like w(w+3) = 40, you must:
Distribute: w² + 3w = 40
Move everything to one side: w² + 3w - 40 = 0

Choose a Solving Method
Once in standard form, you have three primary ways to find the value of x:
Factoring:
Best for “clean” numbers. Find two numbers that multiply to c and add to b.
Quadratic Formula:
Use when numbers are messy or decimals. \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Vertex Formula
Use if the question asks for a maximum or minimum. \(t = \frac{-b}{2a}\).

Interpret the Results (The “Reality Check”)
Quadratic equations usually give two answers. In word problems, one is often “extraneous” (meaning it doesn’t make sense in real life).
Distance/Width: If you get x = 5 and x = -8, discard the -8. You cannot have a negative width.
Time: If you are calculating how long a ball is in the air, discard negative time.
Projectiles: If the math gives you two positive times (e.g., t = 1s and t = 3s), it means the object hit that height once on the way up and once on the way down.

Example Problem:
A rectangular garden has an area of 54m². The length is 3 m more than the width. Find the dimensions.
Define: Let w = width. Then L = w + 3.
Equation: w(w + 3) = 54 → w² + 3w - 54 = 0.
Factor: (w + 9)(w - 6) = 0.
Solve: w = -9 or w = 6.
Check: Since width can’t be negative, width = 6m and length = 9m.
 

This video gives a clear, step-by-step approach to explain how to solve quadratic algebra word problems using cross multiplication.

• Show Video

 

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