Question

PLEASE HELP ASAP

Answer 1

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:

$f(x) = ax^{2} + bx + c$

It's vertex is the point $(x_{v}, y_{v})$

In which

$x_{v} = -\frac{b}{2a}$

$y_{v} = -\frac{\Delta}{4a}$

Where

$\Delta = b^2-4ac$

If a<0, the vertex is a maximum point, that is, the maximum value happens at $x_{v}$, and it's value is $y_{v}$.

In this question:

We have that:

$s(t) = -16t^2 + 48t + 144$

Which is a quadratic equation with $a = -16, b = 48, c = 144$.

The maximum height is the value of s, which is the output, at the vertex. So

$\Delta = b^2-4ac = 48^2 - 4(-16)(144) = 11520$

$s_{v} = -\frac{11520}{4(-16)} = \frac{11520}{64} = 180$

The maximum height attained by the ball is of 180 feet.