Quadratic Applications
Projectile motion, area and optimisation problems.
Key idea
Projectile motion, area and optimisation problems.
In depth
Quadratics model projectiles, areas, and optimisation problems. The vertex gives the maximum or minimum, and the roots give where the quantity is zero, such as when a ball lands.
Worked example
A ball has height h = −5t² + 20t. The peak is at t = 2 s, h = 20 m. It lands when −5t(t − 4) = 0, t = 4 s.
Real-world uses
- Maximising the area of a fenced garden
- Modelling projectile motion in sports and ballistics
Common mistake
Accepting a negative time or length as an answer; check it makes sense.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Quadratic Applications?
Projectile motion, area and optimisation problems. It is a topic at the advanced level in Algebra.
Where is Quadratic Applications used in real life?
Real-world examples: Maximising the area of a fenced garden; Modelling projectile motion in sports and ballistics.
What should I learn before Quadratic Applications?
Make sure you are comfortable with Quadratic Inequalities, the previous topic in Algebra.
What is a common mistake with Quadratic Applications?
Accepting a negative time or length as an answer; check it makes sense.
How can I practise Quadratic Applications?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Quadratic Applications?
Move on to Rational Expressions next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.