Question

A football is passed through the air and caught at ground level for a touchdown. The height of the ball (h) is given by h= -d² + 12d + 6, where d is the distance in feet the ball travels horizontally. How far from the player passing the ball will the ball be caught?
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Answer 1

Answer:

d = 6+sqrt(42)=12.4807407

Step-by-step explanation:

h= -d² + 12d + 6

The ball is caught at ground level  which means h=0

0 =  -d² + 12d + 6

Subtract 6 from each side

-6 = -d^2 +12d

Factor out a - sign

-6 =-(d^2-12d)

Divide by -1

6 = d^2 -12 d

Complete the square

-12/2 = -6  then square it = 36

Add 36 to each side

6+36 = d^2 -12d +36

42 = (d-6)^2

Take the square root of each side

±sqrt(42) = sqrt( (d-6)^2)

±sqrt(42) =  (d-6)

Add 6 to each side

6±sqrt(42) =  (d-6)+6

6±sqrt(42) =  d

d = 6+sqrt(42)=12.4807407

d =6- sqrt(42)=-.480740698

Since the distance cannot be negative