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

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Question 165753: 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.
How high will the football reach its highest point? Why?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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.
How high will the football reach its highest point? Why?
:
Find the axis symmetry of the equation using the formula x - %28-b%29%2F%282a%29
:
In the equation ;f(x)= -.0625x²+2.7x. a=-.0625, b=2.7
x = %28-2.7%29%2F%282%2A-.0625%29
x = %28-2.7%29%2F%28-.125%29
x = +21.6 yds from kickoff line for max height
:
Substitute 21.6 for x in the original equation to find the height
h = -.0625(21.6^2) + 2.7(21.6)
h = -29.16 + 58.32
h = 29.16 yds is max height
:
Why? That's just the nature of a parabola with a negative coefficient of x^2