Question

The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?

Answer 1

convert to vertex form:-
= -0.04(x^2 + 39x)
= -0.04( (x + 19.5)^2 - 380.25)

vertex is at -0.04 * -380.25 = 15.21 yards

Maximum height is about 15.2 yards

Answer 2

Maximum height is 15.21 yards

Explanation:

The path of a football kicked by a field goal kicker can be modeled by the equation
`y = -0.04x^2 + 1.56x`, where x is the horizontal distance in yards and y is the corresponding height in yards

MAximum height occurs at the vertex

Lets find x coordinate of vertex using formula

`x=(-b)/(2a)`

`a=-0.04, b= 1.56`

plug in all the values

`x=(-1.56)/(2(-0.04))=19.5`

To find out maximum heigt, plug in 19.5 for x in the given equation

`y = -0.04x^2 + 1.56x`

`-0.04\left(19.5\right)^2\:+\:1.56\left(19.5\right)=15.21`