Parabola algebra 2

Question

Although a football field appears to be flat, it's surface is actually shaped like a parabola so that rain runs off to either side. The cross section field with synthetic turf can be molded by y=-0.000234(x-80)^2+1.5. Where x and y are measured in feet. What is the fields width? What's the maximum height of the fields surface?

Answer 1

The ends of the field are at the zeros (x-intercept) of the function.

 

0 = -0.000234(x - 80)² + 1.5      subtract 1.5 from both sides

-1.5 = -0.000234(x - 80)²           divide both sides by right coefficient

6410.25641 = (x - 80)²              take square root of both sides

80.064 = x - 80                         add 8-0 to both sides

160.064 = x

 

The field is 160.064 feet wide. 

The maximum is at the vertex, y = 1.5 feet