Question

The opening of the tunnel can be modeled by the graph of the equation y=-0.18x^2+4.4x-12 where x and y are measured in feet. Find the maximum height of the tunnel.

Answer 1

1. To find the vertex of a parabolla whose equation is written in the standard form, you must apply the following proccedure:
 
 2. You have:
 
 y=-0.18x²+4.4x-12 
 
 a=-0.18
 b=4.4
 
 3. You must apply the following formula:
 
 x=-b/2a
 x=-4.4/2(-0.18)
 x=-4.4/-0.36
 x=12.22
 
 4. When you susbtitute x=12.22 into the equation y=-0.18x²+4.4x-12, you obtain:
 
 y=-0.18x²+4.4x-12
 y=-0.18(12.22)²+4.4(12.22)-12
 y=14.88 feet
 
 5. The answer is: The maximum height of the tunnel is 14.88 feet