If h=0 represents the base of the model, then ...
The bridge touches the base of the model at 2 feet and 6 feet from the leftmost edge of the model.
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When in doubt, use your calculator to graph it.
Here, the solution is not so hard. We're looking for h(x) = 0.
Multiply by -2
(x -4)² -4 = 0
(x -4) = ±√4
x = 4 ±2 = {2, 6}