Answer:
[tex]-9.31x^2+56.26x[/tex]
Step-by-step explanation:
Let the quadratic function be:
[tex]h=ax^2+bx+c[/tex]
Where [tex]h[/tex] is the height of soccer ball and
[tex]x[/tex] is the time in seconds.
Initially, at time [tex]x=0\Rightarrow h=0[/tex]
Therefore, [tex]c=0[/tex]
Given that,
[tex]x=3, h=85\\and\\x=6, h=2.5[/tex]
Putting the values and making equations in [tex]a,b[/tex] :
[tex]85=9a+3b\\2.5=36a+6b[/tex]
By solving the above equations, we get:
[tex]a=-9.31\\ and\\b =56.26[/tex]
So, the quadratic expression is:
[tex]-9.31x^2+56.26x[/tex]
