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?
✗ The trap: 3 (the number inside the parentheses).
✓ The fix: 5 — the minimum value of f, reached AT x = 3.
How to actually fix it
- Write the vertex as a labeled point: (h, k) = (3, 5).
- 'Minimum value' = k, the y-coordinate. 'Where' = h.
- Watch the sign of h: (x − 3)² means h = +3, and (x + 3)² means h = −3.
Made this mistake on a real question?
Practice Advanced Math questions here. Miss one and it is logged with the exact error, then brought back until you beat it.
Practice Advanced Math →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.