Quadratic Models
Real-World Applications of Quadratic Functions on the SAT
SAT Math
Algebra
Problem Solving
What Are Quadratic Models?
A quadratic model is a real-world situation described by a quadratic function — a relationship where the output depends on the square of the input.
General Form
$$f(x) = ax^2 + bx + c$$
This models situations with maximum or minimum values and parabolic behavior.
Why Quadratic?
- Projectile motion — a ball thrown in the air
- Area relationships — maximizing a garden's area
- Profit optimization — finding the best price
- Stopping distance — distance ∝ speed²
Key Features in Context
- Vertex → optimal value (max or min)
- x-intercepts → break-even or zero points
- Direction → $a < 0$ means max; $a > 0$ means min
- y-intercept → initial value when $x = 0$
Interactive: Anatomy of a Quadratic Model (Projectile Motion)
Interactive visualization — available in the full lesson
This graph shows a projectile launched from 80 ft with initial velocity 64 ft/s. The vertex gives maximum height; the x-intercept gives landing time.