a Recall that the maximum or minimum point of the graph of a quadratic function is the vertex. Since the function gives the height of the tennis as a function of time, the time when it reaches its maximum height is equal to the horizontal coordinate of the vertex. This coordinate can be obtained by using the formula shown below.
V_t = -b/2aLet's take a look at the function modeling the height of the ball and compare it to the standard form of a quadratic function. This way we can identify the parameters a and b.
at^2+ bt+c
- 4.9t^2+ 3.8t+0.5
As we can see a = - 4.9 and b = 3.8. Now let's find the t-coordinate of the vertex.
Therefore, we can know that the ball reaches the maximum height when t ≈ 0.4seconds.
b Recall that the exercise explains that the tennis player hits the ball and it leaves the racket at 0.5m above the ground. This is why when t=0 the value for the function modeling the height is 0.5.
Therefore, at t=0 the height is 0.5m. According to the results from Part A, at t=0.4seconds the ball is at its maximum height. After another 0.4seconds, when t=0.8seconds the ball will be again a 0.5m, not at the ground! This is due to the symmetry of the parabola.
