Question

The height y (in feet) of a punted football is given by -16/2025x^2 + 9/5x + 2.5 where x is the horizontal distance (in feet) from the point at which the ball is punted.

(a) How high is the ball when it is punted?
(b) What is the maximum height of the punt? (Round your answer to two decimal places.)
(c) How long is the punt? (Round your answer to two decimal places.)

Answer 1

a) The ball is 2.5 feet high when it is punted ( for: x=0 )
b) The maximum height ( formula for the parabola):Ymax=
`(4ac-b^(2) )/(4a)= (4* (-16)/(2025)*25- (9)/(5)^(2) )/(4* (-16)/(2025) )`
Finally: Ymax= 105.02 feet.
c)We will find how long is the punt with the formula:

`- (16)/(2025) x^(2) + (9)/(5)x +2.5=0`
We will multiply it by 2025 to avoid the fractions:

`-16 x^(2) +3645x+5062.5=0`
And we will solve it:

`x_(12) = \frac{-b\pm \sqrt{b^(2) -4ac} }{2a}= (-3645\pm √(13286025+324000) )/(-32) x_(1)= (-3645-3689.1767)/(-32)`
x=229.19 feet.
We will except this answer because another one is negative.