Answer
(For this question, units are in feet)
It's basically a graphing question
- the x-axis represents the surface of the water
- the shape of the graph is the same as the shape of the arch
First, find out x-interception (y=0)
when y=0
-0.628x^{2}+4.5x=0
x(-0.628x+4.5)=0
x=0 or -0.628x+4.5=0
-0.628x=-4.5
x=\frac{-4.5}{-0.628}
x=7.17
therefore x-intercept (0,0) and (7.17,0)
Work Step by Step
Second, find the turning point
the x corrdinate of the turning point is the midpoint of the x-intercept
therefore $(0+7.17)\div2=3.56$
x=3.56
sub x=3.56 into the equation
$y=(-0.628)\times3.56x^{2}+4.5\times3.56$
y=8.06
therefore the turning point is (3.56, 8.06)
So, when the water level rises by 5.5 feet
$5.5\lt8.06$
therefore, the top of the arch support is above the water
