SOLUTION: Why is the vertex of a parabola important to us? Specifically, what kind of information does the vertex give us? In your explanation include a real-world example where a quadra

Question 381887: Why is the vertex of a parabola important to us? Specifically, what kind of information does the vertex give us? In your explanation include a real-world example where a quadratic model is appropriate, identify the vertex, and explain what the vertex represents. (TEXTBOOK)
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Suppose you kick a football and it follows a trajectory. The height X will be modeled by a quadratic function because (well, I need calculus to explain why it's quadratic):

Hence, X is a quadratic function in terms of t. The vertex represents the time t where the maximum height is attained, and X(t) gives the maximum height (assuming air resistance is negligible).
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