Quadratic Functions & Parabolas
The vertex form y = a(x − h)² + k shows the vertex (h, k).
The rules
- The vertex of y = ax² + bx + c is at x = −b/(2a).
- If a > 0 the parabola opens up (minimum at the vertex). If a < 0 it opens down (maximum).
- The axis of symmetry is x = h.
- The y-intercept is c.
Watch out: Reading the vertex's x-coordinate with the wrong sign.
Worked example
What is the minimum value of f(x) = x² − 6x + 11?
- Vertex x = 6/2 = 3.
- f(3) = 9 − 18 + 11 = 2.
Answer: 2
Try it yourself
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