Respuesta :
Answer:
The maximum height that the object will reach is of 9 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
In this question:
[tex]f(t) = -16t^{2} + 16t + 5[/tex]
So
[tex]a = -16, b = 16[/tex]
The instant of the maximum height is:
[tex]t_{v} = -\frac{16}{2*(-16)} = 0.5[/tex]
The maximum height is:
[tex]f(0.5) = -16*(0.5)^2 + 16*0.5 + 5 = 9[/tex]
The maximum height that the object will reach is of 9 feet.
