The quadratic function modeling the helght of a ball over time is symmetric about the line t = 2.5, where is lite
Is true about this situation?

A. The height of the ball is the same after 1.5 seconds and 3.5 seconds.

B. The height of the ball is the same after 1 second and 3 seconds.

с. The height of the ball is the same after 0.5 second and 5.5 seconds.

D. The height of the ball is the same after 0 seconds and 4 seconds.

The average of the x-coordinates of any opposite points (points have the same y-coordinates) on the parabola is equal to the x-coordinate of its vertex point.

The axis of symmetry of it passes through the x-coordinate of its vertex point.
The equation of its axis of symmetry is x = h, where h is the x-coordinate of its vertex point.

∵ The quadratic function modeling the height of a ball over time

∴ f(t) = at² + bt + c

→ t is the time in second, f(t) is the height of the ball after t seconds

∵ It is symmetric about the line t = 2.5

∴ The x-coordinate of its vertex is 2.5

→ That means the average of the x-coordinates of any two

opposite points belong to f(t) is 2.5

∵ The average of 1.5 and 3.5 = [tex]\frac{1.5+3.5}{2}=\frac{5}{2}=2.5[/tex]

∴ 1.5 and 3.5 have the same value of f(t)

∴ 1.5 and 3.5 have the same height

The height of the ball is the same after 1.5 seconds and 3.5 seconds.