Respuesta :
D. the h coordinate of the vertex is the balls maximum height
Answer:
The maximum height of the ball is 19.9 meters after 1 second.
Step-by-step explanation:
The height of a ball represents by the function
[tex]h(t) = -4.9t2 + 9.8t + 15[/tex]
where, h(t) is the height in meters, of the ball above the ground at the base of the hill and the time t, in seconds, after the ball is thrown.
In the given equation leading coefficient is -4.9 which is a negative number. So, it is a downward parabola and vertex of a downward parabola represents the maximum value of the function.
It means vertex of the given function represents the maximum height of the ball.
If a quadratic function is defined as
[tex]f(x)=ax^2+bx+c[/tex]
then vertex of the function is
[tex]Vertex=(-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]
In the given function, [tex]a=-4.9,b=9.8,c=15[/tex].
[tex]-\frac{b}{2a}=-\frac{9.8}{2(-4.9)}=1[/tex]
Substitute t=1 in the given function.
[tex]h(1) = -4.9(1)2 + 9.8(1) + 15=19.9[/tex]
The vertex of the function is (1,19.9).
Therefore, the maximum height of the ball is 19.9 meters after 1 second.
