a When a ball is kicked, it follows a parabolic route. It first rises for a certain period of time until it reaches the maximum height and then it begins to fall.
B
b Use the flight time that you found in Part A.
C
c Use the x-vertex that you found in Part A.
A
a 3 seconds
B
b 48 meters
C
c 11.025 meters
Practice makes perfect
a When a ball is kicked, it follows a parabolic route. It first rises for a certain period of time until it reaches the maximum height and then it begins to fall. Let's model this situation.
The x-coordinate of the vertex will give us the rise time. We can find it by using the formula for the axis of symmetry, t= - b2a. Let's rewrite the function in the general form of a quadratic function to determine a and b.
f(x)= ax^2+ bx+ c
⇓
h(t)= -4.9t^2+ 14.7t+ 0
Now, we can find the rise time.
The ball travels 48 meters before it hits the ground.
c The maximum height of the ball will be on the vertex of its parabolic route. We found the x-coordinate of the vertex in Part A as t= 32. By substituting this value into the height function, we can find the maximum height.
