Math

Parabola Calculator

The vertical line x = −b/(2a) through the vertex.

Find the vertex, axis and direction of y = ax² + bx + c.

Calculated Output

Vertex x 2

Vertex y -1

Opens up(1)/down(−1) 1

Formula: vertex x = −b/2a, vertex y = c − b²/4a

Step-by-Step Breakdown

1. Values used:

2. a = 1

3. b = -4

4. c = 3

6. Vertex x = 2

7. Vertex y = -1

8. Opens up(1)/down(−1) = 1

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The math behind it

The vertex sits at x = −b/(2a). If a > 0 the parabola opens upward (minimum); if a < 0 it opens downward (maximum).

y = x² − 4x + 3 → vertex (2, −1), opens up.

What is the axis of symmetry?

The vertical line x = −b/(2a) through the vertex.