In y = a(x − h)^2 + k, the parameter a determines which aspect?

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Multiple Choice

In y = a(x − h)^2 + k, the parameter a determines which aspect?

Explanation:
In the vertex form y = a(x − h)^2 + k, the vertex is fixed at (h, k), but the parameter a controls how the graph behaves vertically. If a is positive, the parabola opens upward; if a is negative, it opens downward. The magnitude of a determines the width: larger |a| makes the parabola narrower and steeper, while smaller |a| makes it wider and more shallow. The axis of symmetry is the vertical line x = h, so that part does not change with a.

In the vertex form y = a(x − h)^2 + k, the vertex is fixed at (h, k), but the parameter a controls how the graph behaves vertically. If a is positive, the parabola opens upward; if a is negative, it opens downward. The magnitude of a determines the width: larger |a| makes the parabola narrower and steeper, while smaller |a| makes it wider and more shallow. The axis of symmetry is the vertical line x = h, so that part does not change with a.

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