SOLUTION: An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is       Log On


   

Question 166632: An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and the f(x) is the vertical distance the football travels. The bottom of the uprights is 3.5 yards above the ground.
1. Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not?
2. Would the kicker have made a 42-yard field goal with the same kick? Why or Why not?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and f(x) is the vertical distance the football travels. The bottom of the upright is 3.5 yards above the ground.
Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not?
:
Find value of (x) (dist) when f(x) = 3.5 (height)
-.0625x² + 2.7x = 3.5
:
-.0625x² + 2.7x - 3.5 = 0
:
Use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem a=-.0625; b=+2.7; c=-3.5
x+=+%28-2.7+%2B-+sqrt%282.7%5E2+-+4+%2A+-.0625+%2A+-3.5+%29%29%2F%282%2A-.0625%29+
:
x+=+%28-2.7+%2B-+sqrt%287.29+-+.875%29%29%2F%28-.125%29+
:
x+=+%28-2.7+%2B-+sqrt%286.415%29%29%2F%28-.125%29+
:
x+=+%28-2.7+%2B+2.533%29%2F%28-.125%29+
x+=+%28-.167%29%2F%28-.125%29+
x = 1.33; not the solution we want here
and
x+=+%28-2.7+-+2.533%29%2F%28-.125%29+
x+=+%28-5.233%29%2F%28-.125%29+
x = 41.86 yds; clears the upright nicely
:
The ball had traveled almost 42 yds when it had descended to 3.5 meters
:
:
2. Would the kicker have made a 42-yard field goal with the same kick? Why or Why not?.
Find the height at 42 yds
h = -.0625x² + 2.7x
Substitute 42 for x
h = -.0625(42^2) + 2.7(42)
h = -.0625(1764) + 113.4
h = -110.25 + 113.4
h = 3.15 yds, So No; just under the bar at 3.5 yds high