Quadratic Word Problems
Quadratics model areas, projectile heights and profit.
About this topic
Quadratic word problems describe situations with squared quantities: areas, falling or thrown objects, revenue, and number puzzles. Define a variable, write an equation, choose a solving method, then interpret the answers in context.
Reject solutions that do not make sense, such as a negative length or time. Example: a rectangle's length is 3 more than its width and its area is 40. With width w, w(w + 3) = 40 leads to w² + 3w − 40 = 0, which factors as (w + 8)(w − 5), so w = 5 and the length is 8; the root −8 is rejected. For a ball thrown upward, h = −16t² + 48t + 4 gives the time of flight when h = 0 and the maximum height at the vertex.
Such models appear in sports, construction, fencing a field with the most area, and pricing to maximize revenue.
The usual difficulties are translating words into an equation and forgetting to answer the question asked. Draw a diagram, label the unknowns with units, check that your answer satisfies the original statement, and write a sentence with units. A maximum or minimum question needs the vertex, while a question about when something happens needs the roots.
Key ideas
- Define variables and write the equation
- Use the vertex for maximum or minimum
- Choose answers that make sense
Quick check
Use cases: where Quadratic Word Problems helps
- Homework: review the key idea behind Quadratic Word Problems before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Quadratic Word Problems without notes.
- Visual learning: play with the interactive lab to see how Quadratic Word Problems changes when you adjust its inputs.
- Teaching a friend: explain Quadratic Word Problems in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Quadratic Word Problems?
Quadratics model areas, projectile heights and profit.
What will I learn in Quadratic Word Problems?
Define variables and write the equation. Use the vertex for maximum or minimum. Choose answers that make sense.
Is Quadratic Word Problems part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Quadratic Word Problems lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Quadratic Word Problems?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.