Respuesta :
Answer:
The ball reaches maximum height in 3 seconds.
The maximum height of the ball is of 400 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:
The height is modeled by:
[tex]s(t) = -16t^2 + 96t + 256[/tex]
So, the coefficients are:
[tex]a = -16, b = 96, c = 256[/tex]
Instant of time the ball reaches maximum height:
[tex]t_{v} = -\frac{96}{2(-16)} = -\frac{96}{-32} = 3[/tex]
The ball reaches maximum height in 3 seconds.
What is the maximum height of the ball?
This is s(3).
[tex]s(3) = -16t^2 + 96t + 256 = -16*3^2 + 96*3 + 256 = 400[/tex]
The maximum height of the ball is of 400 feet.
