Respuesta :
Answer:
The maximum height attained by the ball is of 180 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}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/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]y_{v}[/tex].
In this question:
We have that:
[tex]s(t) = -16t^2 + 48t + 144[/tex]
Which is a quadratic equation with [tex]a = -16, b = 48, c = 144[/tex].
The maximum height is the value of s, which is the output, at the vertex. So
[tex]\Delta = b^2-4ac = 48^2 - 4(-16)(144) = 11520[/tex]
[tex]s_{v} = -\frac{11520}{4(-16)} = \frac{11520}{64} = 180[/tex]
The maximum height attained by the ball is of 180 feet.
