Can somebody help/teach me about this please?“Suppose the equation h=-16t^2 + 35t models the altitude a football will reach t seconds after it is kicked. IS THE GIVEN VALUE POSSIBLE?” A: h= 16 ft. B: h= 20ft.

A. Since we know that [tex]h[/tex] is the altitude a football will reach t seconds after it is kicked, we are going to replace the altitude [tex]h=16[/tex] in our equation and solve for [tex]t[/tex]. If the equation has any positive real solutions, we can conclude that the given value is possible. 

We know from our problem that the given value is [tex]h=16[/tex], so lets replace that value in our equation and solve for [tex]t[/tex]:
[tex]h=-16t^2+35t[/tex]
[tex]16=-16t^2+35t[/tex]
[tex]16t^2-35t+16=0[/tex]
Solving for [tex]t[/tex]:
[tex]t=1.54[/tex] or [tex]t=0.65[/tex]

We can conclude that the given value, h=16, is possible. In fact, the ball reaches that height two times: at [tex]t=0.65[/tex] and [tex]t=1.54[/tex].

B. Just like before, we are going to replace the given value, [tex]h=20[/tex], in our equation [tex]h=-16t^2+35t[/tex], and then, we are going to solve for [tex]t[/tex] to check if the given value is possible. If the equation has any positive real solutions, we can conclude that the given value is possible.
[tex]h=-16t^2+35t[/tex]
[tex]20=-16t^2+35t[/tex]
[tex]16t^2-35t+20=0[/tex]
Solving for [tex]t[/tex]:
[tex]t= \frac{35+i \sqrt{55}}{32} [/tex] or [tex]t= \frac{35-i \sqrt{55}}{32} [/tex]

Since the equation doesn't have any real solutions, we can conclude that the given value, h=20, is not possible.