Respuesta :
Answer:
The maximum height the soccer ball reaches is 9.77 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].
Reba kicks a soccer ball off the ground and in the air, with an initial velocity of 25 feet per second.
The formula for the height is:
[tex]h(t) = -16t^2 + v(0)t + h(0)[/tex]
In which v(0) is the initial velocity and s(0) is the initial height.
Initial velocity of 25 feet per second means that [tex]v(0) = 25[/tex]
Kicked off the ground means that [tex]h(0) = 0[/tex]. So
[tex]h(t) = -16t^2 + 25t[/tex]
Which is a quadratic equation with [tex]a = -16, b = 25, c = 0[/tex].
The maximum value is:
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
In which
[tex]\Delta = b^2-4ac = 25^2 - 4(-16)(0) = 625[/tex]
[tex]y_{v} = -\frac{\Delta}{4a} = \frac{625}{4(16)} = 9.77[/tex]
The maximum height the soccer ball reaches is 9.77 feet.
