Answer:
A quadratic equation is of the form [tex]y=ax^2+bx+c[/tex] ...[1] then the axis of symmetry is given by:
[tex]x = -\frac{b}{2a}[/tex]
As per the statement:
The ball travels on a parabolic path represented by the equation is:
[tex]h= -8t^2+40t[/tex] ....[2]
where,
h represents the height of the ball above the ground
t represents the time in seconds.
To find how many seconds does it take the ball to reach its highest point.
On comparing with [1] we have;
a = -8 and b = 40
then:
axis of symmetry is :
[tex]t =-\frac{40}{2(-8)} = \frac{40}{16} = 2.5[/tex] sec
⇒2.5 seconds does it take the ball to reach its highest point.
Substitute the value of t =2.5 sec in [2] we have;
[tex]h = -8(2.5)^2+40(2.5) = -50+100 = 50[/tex]
Ordered pair = (2.5, 50)
Therefore, (2.5, 50) ordered pair represents the highest point that the ball reaches as it travels through the air
