Question

A soccer ball is punted in the air. Its height after x seconds can be modeled by a quadratic function. The soccer ball reaches its maximum height of 85 feet after 3 seconds. The ball is trapped at a height of 2.5 feet, 6 seconds after being kicked. Write a quadratic function that models the height of the soccer ball, x seconds after being kicked.

Answer 1

`-9.31x^2+56.26x`

Explanation:

Let the quadratic function be:

`h=ax^2+bx+c`

Where
`h` is the height of soccer ball and

`x` is the time in seconds.

Initially, at time
`x=0\Rightarrow h=0`

Therefore,
`c=0`

Given that,

`x=3, h=85\\and\\x=6, h=2.5`

Putting the values and making equations in
`a,b` :

`85=9a+3b\\2.5=36a+6b`

By solving the above equations, we get:

`a=-9.31\\ and\\b =56.26`

So, the quadratic expression is:

`-9.31x^2+56.26x`