document.write( "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) \n" ); document.write( "

Algebra.Com's Answer #270890 by richard1234(7193) $\"\"$ $\"About$

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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):\r
\n" ); document.write( "\n" ); document.write( " $\"V+=+int%28a%2C+dt%29+%2B+v_0+=+at+%2B+v_0\"$ \r
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\n" ); document.write( "\n" ); document.write( "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). \n" ); document.write( "

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