Reading the minimum from vertex form: the sign trap in (x − h)²
Vertex form hands you the vertex (3, 5), then asks for the minimum value. Answering 3 — the x-coordinate — is the most-picked wrong answer.
Why it happens
Two numbers sit in the formula and the question asks for one number. Without labeling which coordinate is which, the first number wins.
See the trap
What is the minimum value of f(x) = (x − 3)² + 5?
3 (the number inside the parentheses).
5 — the minimum value of f, reached AT x = 3.
How to actually fix it
- 1Write the vertex as a labeled point: (h, k) = (3, 5).
- 2'Minimum value' = k, the y-coordinate. 'Where' = h.
- 3Watch the sign of h: (x − 3)² means h = +3, and (x + 3)² means h = −3.
Practice this trap · 4 real questions
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
FAQ
When is it a maximum instead?
When the squared term is negative — f(x) = −(x − h)² + k opens downward, so k becomes the maximum value.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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