a How can you interpret the coordinates of the vertex?
B
b Equate the function and 0.6. Solve the equation, and remember that the player hit the ball on its way down.
A
a 2.45 meters
B
b About 1.3 seconds
Practice makes perfect
a The function below models the height h of the tennis ball in meters from the point of the toss after t seconds.
h(t)=-5t^2+7tTo find the maximum height reached by the ball, we need to find the maximum point on the graph of y=h(t). Since the leading coefficient of h(t) is negative (-5), its graph is a parabola that opens downward. This means the maximum point is the vertex. Let's find its t-coordinate.
t = -b/2a ⇒ t = -7/2(-5) = 0.7
To find the h-coordinate, we substitute t=0.7 into h(t).
We got two different times at which the ball was 0.6 meters from the point of the toss. From Part A, we know the ball reached the maximum height at 0.7 seconds. This means that at t_1=0.1 seconds the ball was going up, and at t_2=1.3 seconds the ball was going down.
In conclusion, the ball remained in the air for approximately 1.3 seconds between the toss and the serve.
