The vertex of a parabola always gives either the maximum y value (if the parabola opens down) or minimum value (if the parabola opens up.) The vertex also lies along the vertical axis of symmetry. To find the vertex, here in the context of the maximum height that an object attains, you could either complete the square or use t = -b/2a. Here we use the second method to find the vertical axis of symmetry, and then plug that time value to plug back in and find the maximum height. This method can be extended to any maximum (like profit, sales, area etc.) or minimum (like cost).
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