Answer:
Step-by-step explanation:
The given function is
[tex]y=-x^{2} +4x+5[/tex]
The given function models the path of the ball.
The maxium height the ball reached is given by the vertex of this function, which has coordinates [tex]V(h,k)[/tex], where [tex]h=-\frac{b}{2a}[/tex] and [tex]k=f(h)[/tex].
From the equation, we know that [tex]a=-1[/tex], [tex]b=4[/tex] and [tex]c=5[/tex]. Replacing these values, we have
[tex]h=-\frac{4}{2(-1)}=2[/tex]
[tex]k=f(2)=-(2)^{2} +4(2)+5=-4+8+5=9[/tex]
Where [tex]k[/tex] determines the height and [tex]h[/tex] the time when the maximum height was reached by the ball.
The maximum height is 9 units.
Therefore, after two seconds, the ball reached 9 units up.
