Mon Prof Augmenté
Upward and downward parabolas
Age 16 · Maths
A quadratic function y = ax² + bx + c graphs as a parabola. The sign of a decides whether the curve opens upward or downward, and its vertex is the lowest or highest point on a vertical axis of symmetry.
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Age 16: open this week
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In the picture
- Blue curve: a positive a opens upward.
- Red dot at the lowest point: the minimum vertex.
- Orange curve: a negative a opens downward.
- Red dot at the highest point: the maximum vertex.
- Dashed vertical line through a vertex: the axis of symmetry.
Examples
- the curved path of a thrown ball
- the shape of water in a fountain
Key takeaways
- The sign of a controls whether a parabola opens upward or downward.
- The vertex is the minimum when a > 0 and the maximum when a < 0; the axis of symmetry is vertical through it.
Quiz: Upward and downward parabolas (Age 16)
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For a quadratic function y = ax² + bx + c, what does the sign of a determine?
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When a is positive (a > 0), what is the vertex of the parabola?
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How is the axis of symmetry of a parabola positioned?
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