Answer :
Answer:
92 feet
Explanation:
Given the speed of the arrow as 64 feet per second and the height of the platform as 28 feet.
Given the below function;
[tex]h(t)=-16t^2+64t+28[/tex]The above is given in the form of a quadratic function;
[tex]f(x)=ax^2+bx+c[/tex]If we compare both functions, we can see that a = -16, b = 64 and c = 28.
Since the motion of the arrow is modeled by a quadratic function, it means that it will take the shape of a parabola.
The x-coordinate of the maximum point(vertex) of a parabola is generally determined by the below formula;
[tex]x=\frac{-b}{2a}[/tex]Let's go ahead and determine t at maximum point by substituting the above values into our vertex formula;
[tex]t=\frac{-64}{2(-16)}=\frac{-64}{-32}=2[/tex]To determine the maximum height, all we need to do is substitute t = 2 into the given equation of a parabola and solve for h;
[tex]\begin{gathered} h(2)=-16(2)^2+64(2)+28 \\ =-64+128+28 \\ =92ft \end{gathered}[/tex]We can see from the above that the maximum height of the arrow will be 92ft
