SAT Math: Interpreting the Vertex in Context
39+ practice questions in Praczo
The concept, explained
- 1
In a real-world quadratic model (like a projectile in the air or profit of a company), the vertex represents the MAXIMUM or MINIMUM value.
- 2
The x-coordinate of the vertex tells you WHEN the max/min happens (e.g., at 3 seconds, or at a $5 price point).
- 3
The y-coordinate of the vertex tells you WHAT the actual max/min value is (e.g., 100 feet high, or $5000 in profit).
- 4
The SAT loves to ask questions where students incorrectly give the x-value when the prompt asked for the y-value (or vice versa).
- ✗ Solving for the x-intercepts (when the projectile hits the ground) instead of the vertex (when it peaks).
- ✗ Providing the time the max height was reached instead of the height itself.
SAT-style practice
A toy rocket's height h(t) after t seconds is modeled by h(t) = -16(t - 2)² + 64. What is the maximum height reached by the rocket?
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