DDesmos SAT Prep
← All categories

Vertex Form & Max/Min

Find the maximum or minimum of a quadratic without completing the square.

The Desmos trick

Graph the function and click on the highest or lowest point of the parabola. Desmos labels it as the exact vertex — perfect for projectile motion and revenue/profit problems.

  • Type the model as given, e.g. y = -16x^2 + 64x + 5
  • Click directly on the peak (or valley) of the curve to snap to the vertex
  • Rename x and y to match the problem's variables if it helps you stay organized, e.g. h(t) = ...

Practice questions

Q1A ball's height in feet is given by h(t) = -16t^2 + 64t + 5, where t i…
Medium
Q2A company's weekly profit, in dollars, is modeled by P(x) = -5x^2 + 30…
Hard
Q3What is the minimum value of y = (x - 2)^2 - 9?
Easy
Q4A ball's height in feet is modeled by h(t) = -16t^2 + 48t, where t is …
Medium