Answer
$16~ft$
Work Step by Step
Find the $y$ of the vertex, that is:
$f(-\frac{b}{2a})=f(-\frac{\frac{24}{9}}{2(-\frac{4}{9})})=f(3)$
$f(3)=-\frac{4}{9}(3)^2+\frac{24}{9}(3)+12=-4+8+12=16$
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