Quadratic Applications
A free Algebra II lesson from the “Trigonometry and Modeling” unit, with a worked example and practice problems including step-by-step solutions.
Quadratic applications often ask about maximum or minimum values, when something reaches the ground, or dimensions that create an area. The vertex and zeros carry the meaning.
What you'll learn
- Model projectile and area contexts
- Use zeros and vertices
- Choose a quadratic strategy
Worked example
Problem. A height model is h(t) = -t^2 + 8t. When does the object hit the ground after launch?
- Set h(t) = 0.
- Factor -t(t - 8) = 0.
- The later time is t = 8.
Answer: 8
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. For h(t) = -t^2 + 10t, when does the maximum occur?
Show solution
- The zeros are 0 and 10.
- The vertex is halfway at 5.
Answer: 5
2. For h(t) = -t^2 + 12t, when does the object return to the ground after launch?
Show solution
- Factor -t(t - 12).
Answer: 12
3. A rectangle has sides x + 2 and x + 8. If x = 4, what is the area?
Show solution
- The side lengths are 6 and 12.
Answer: 72
4. A quadratic has zeros 3 and 15. What is the axis of symmetry?
Show solution
- Average the zeros.
Answer: 9
5. A revenue model opens down. Its vertex represents the...
Choices: Maximum revenue · Minimum revenue · Input only · No solution
Show solution
- Opening down means the vertex is highest.
Answer: Maximum revenue
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