In a Football League game, the path of the football at one particular kick-off can be modeled using the function h(d) = -0.02d^2 + 2.6d - 66.5, where h is the height of the ball and d is the horizontal distance from the kicking team's goal line, both in yards. A value of h(d) = 0 represents the height of the ball at ground level. What horizontal distance does the ball travel before it hits the ground?

Question

campbell_st · Answer

you need to solve the quadratic

$$h(d) = -0.2(d^2 - 130d + 3325) = -0.02(d -35)(d - 95)$$

if height = 0 the ball is on the ground

 then the ball is on the ground at d = 35 then d = 95

it travels 60 units horizontally

anonymous · Answer

How did you find a perfect square with such large numbers

anonymous · Answer

@campbell_st

anonymous · Answer

Do you have a systematic method?

campbell_st · Answer

its not a perfect square.. I removed the common factor of - 0.02.... as that was the ugly part of the quadratic.... 

then when I say the constant as 3325.... I knew the 2 factors would end in 5.... so just an elimination process to find 2 factors of 3325 that added to the -130.... both factors had to be negative.