Completing the square to find a vertex is a proud tradition — and on a timed test, an unnecessary one. Desmos marks every notable point the moment the curve is drawn.
The move: Graph it, tap the special point.
Why it works: The calculator already computed every key point when it drew the graph; tapping just reads off coordinates you'd otherwise derive by hand.
The pattern
- Type the function as y =
- Graph it
- Tap the vertex / zero / intercept you need
Worked example: What is the sum of the zeros of y = x² − 5x + 6?
- Type the function. The parabola appears instantly.
y=x^2-5x+6 - Tap the curve — gray dots pop up on the zeros. Tap each: x = 2 and x = 3.
- 2 + 3 = 5. No factoring, no quadratic formula.
Worked example 2: What is the minimum value of y = x² − 6x + 11?
- Graph it.
y=x^2-6x+11 - Tap the curve — the gray dot at the bottom is the vertex: (3, 2).
- “Minimum VALUE” means the y-coordinate: 2. (Choice 3 is the trap — that's the x.)
Remember it on test day
Graph it, tap it. That's the whole cue — say it when you see this question type and the steps follow.
When this isn't the move
Vertex form conversions (rewrite in a(x−h)²+k form) ask for the expression itself, not the point — that's an equivalent-expressions job.
Drill it until it's reflex
This move is one of Desvantage's 18 training modules: a plain-English lesson, a type-it-yourself walkthrough inside a live Desmos calculator, and a 100-question drill bank that deals ten fresh questions per round. The first two modules — plus the 12-question diagnostic — are free.