SATMediumFrequency: 2 - 3 questions
Quadratic Vertex Form & Maximum/Minimum Word Problems
Parabolas appear in standard form y = ax² + bx + c, vertex form y = a(x - h)² + k, and factored form y = a(x - p)(x - q). The vertex (h, k) represents the maximum when a < 0 and minimum when a > 0. The x-coordinate of the vertex is given by x = -b / (2a).
Core Formula & Concept Cheat Sheet
1x_vertex = -b / (2a)
2Vertex form: y = a(x - h)² + k with vertex (h, k)
3Sum of roots: -b / a, Product of roots: c / a
Desmos Speed-Run Trick
Graph y = ax^2 + bx + c. Desmos automatically highlights the vertex with a clickable gray dot. Click it to read (h, k) directly in 2 seconds.
The 700+ Score Trap
Confusing what the question asks for: the x-value (when/input) versus the y-value (maximum height/output).
Test Your Mastery
Official Exam FormatLive Interactive Practice Drill
A projectile is launched from ground level. Its height h, in meters, after t seconds is modeled by h(t) = -5t² + 40t. At what time t does the projectile reach its maximum height?
Frequently Asked Questions
How do I know if the vertex is a minimum or maximum?
If leading coefficient a > 0, parabola opens upward, giving a minimum. If a < 0, it opens downward, giving a maximum.