Quadratic Word Problems – Real-World Applications
Everything covered in this section – expressions, factoring, completing the square, parabolas, and the vertex formula – comes together in real-world quadratic word problems. These questions typically describe a situation that changes over time or with a variable (like a ball's height, or a fenced-in area), and ask you to find its maximum or minimum value – exactly the vertex y-value from the previous page.
The key skill is translating the story into a quadratic equation first, then applying the vertex formula to find the optimal value – the same translate-then-solve process you've used for every word-problem type throughout this course.
Solving Quadratic Word Problems
Translate the story into a quadratic equation, then find the vertex to answer questions about a maximum or minimum value.
Maximum occurs at t = 6 ÷ 2 = 3 seconds. h = −(3)² + 6(3) = −9 + 18 = 9 m.
Real-Life Application
- Sports science: finding the maximum height of a jump, throw, or kick.
- Construction: finding the dimensions that maximise a fenced or paved area.
- Business: finding the price point that maximises revenue.
Key Takeaways
- Quadratic word problems ask for a maximum or minimum value.
- Translate the story into a quadratic equation, then use the vertex formula.
- This applies every quadratic skill from earlier in this section to real situations.
Practice: Quadratic Word Problems
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