PEAZIT Aha card
Go straight to resources ↓Parabolas: read the vertex from the square
A square is at least 0, attained at x = h. For a > 0 the lowest point is (h, k); for a < 0 it is the highest point.
| Expression | Meaning |
|---|---|
| x = 2 → y = 1 | The bracket is zero: the vertex is (2, 1). |
| x = 1; x = 3 → y = 2 | Equal distance from 2 gives equal y. |
| x = 0; x = 4 → y = 5 | The axis of symmetry is x = 2. |
One worked example
- x = 2 → y = 1The bracket is zero: the vertex is (2, 1).
- x = 1; x = 3 → y = 2Equal distance from 2 gives equal y.
- x = 0; x = 4 → y = 5The axis of symmetry is x = 2.
Watch out: For a < 0, the parabola has a maximum, not a minimum over all real x. In (x + 2)², h = −2.
Goal, prerequisites and card origin
What you will learn: Find the vertex and minimum from y = a(x − h)² + k.
What you need first: Squares and point coordinates.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
A square is at least 0, attained at x = h. For a > 0 the lowest point is (h, k); for a < 0 it is the highest point.