Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The quadratic function is represented by a parabola

• The parabola is symmetric about its vertex.

• 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 = $\frac{1.5+3.5}{2}=\frac{5}{2}=2.5$

∴ 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.