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Finding Maximum Height Using the Vertex of a Parabola
The formula for the height of an object shot upwards with initial velocity and initial height after seconds is . This is a quadratic equation in the variable , so its graph is a parabola. Because the squared term's coefficient () is negative, the parabola opens downward, meaning it has a maximum value. By solving for the coordinates of the vertex, one can find how long it will take the object to reach its maximum height (the -coordinate) and the maximum height itself (the -coordinate).
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Ch.10 Quadratic Equations - Elementary Algebra @ OpenStax
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Finding Maximum Height Using the Vertex of a Parabola
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