The function given by
represents the height of a ball, in feet,
seconds after it is thrown. To the nearest foot, what is the maximum height the ball reaches?
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The correct answer is D.
One way to determine the maximum height the ball reaches is to rewrite the quadratic expression that defines the function by completing the square:
It is not necessary to simplify any further, as the maximum height must correspond to , which is the only value of
that makes the term
nonnegative. By substitution,
. Therefore, to the nearest foot, the maximum height the ball reaches is
feet.
Alternatively, one can use a graphing calculator to determine the maximum value of the function . Since
,
and
, the maximum value of
must occur for some
between
and
. Set the window so that the independent variable goes from
to
and the dependent variable goes from
to
to view the vertex of the parabola. Upon tracing the graph, the maximum value of
is slightly greater than
. Therefore, to the nearest foot, the maximum height the ball reaches is
feet.