Quadratic Word Problems Practice Test

About This Quadratic Word Problems Practice Test

This test emphasizes translation from words to equations. The problems use area, consecutive integers, projectile motion, revenue, fencing, right triangles, and square-root models.

Each solution explains why a negative or otherwise infeasible algebraic root may need to be rejected after the quadratic is solved.

Skills Covered

Building quadratic equations, factoring, square-root methods, vertex optimization, physical constraints, dimensions, motion, and revenue.

Key Ideas

1. Define the variable before writing the model.
2. Move all terms to one side before factoring.
3. Check dimensions and time values for feasibility.
4. A vertex answers maximum or minimum questions.

Common Mistakes to Avoid

Do not report the parameter x when the requested dimension is x−2 or x+5, and do not keep negative lengths or negative times.

Practice Format

Each question has four answer choices. The explanation shows the method, completes the algebra, states the conclusion, and explains why every distractor is incorrect.