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📈 Quadratic Function Graph Lab

Change a, b, and c —
how does the parabola move?

In y = ax² + bx + c, adjust the three constants with the sliders. a decides how wide the parabola opens and which way it faces; b and c decide where it sits.

An equation of the form y = ax² + bx + c is called a quadratic function. Graph it, and you get a smooth U-shaped or upside-down-U-shaped curve called a parabola. The path a thrown ball traces through the air, or the arc of water shooting from a fountain, is very close to a parabola too.

The three constants each play a different role. a decides whether the parabola opens upward or downward, and how narrow or wide it opens (positive a opens upward, negative a opens downward). b and c decide where the parabola sits on the screen, and c in particular tells you right away where the graph crosses the y-axis (its value when x=0). Change a, b, and c one at a time with the sliders, and see for yourself how the parabola's shape and position change.

a (coefficient of x²)1
b (coefficient of x)0
c (constant term)0
y = 1x² + 0x + 0
Vertex: (0, 0) · Axis: x = 0