Afootball kicked straight up from the ground with an initial velocity of 32 ft/s returned to the ground after 2 s. the height of the projectile t seconds after launch is modeled by the function f(x)=-16x^2+32x. what is the maximum height of the projectile in feet? show your work

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: