Answer:
The height of the ball is the same after 1.5 seconds and 3.5 seconds. ⇒ (A)
Step-by-step explanation:
<em>The quadratic function is represented by a parabola</em>
- 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 =
∴ 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.