QF - Applications of Quadratic Functions (Lesson)

Applications of Quadratic Functions

Previously, you did some problem solving with quadratic functions and area.  One of the most common applications of quadratic functions has to do with vertical motion. Vertical motion allows us to use quadratic functions to model the height of an object with respect to how long it's been in the air.

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Applications of Quadratic Functions Practice One

The image below shows the path of an object with time measured in seconds and height measured in feet.

 

1. Based on the graph above, estimate how long it takes the object to reach the ground.
2. Estimate the maximum height of the object. 
3. About how high was the object when it was launched? 
4. Estimate the time when the object reached its maximum height.

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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Watch this video to try one together:

 

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Applications of Quadratic Functions Practice Two

An object is launched directly upward from a platform. The equation that models the height as a function of time is $h(t)=-16t^2+64t+80$

1. From what height was the object launched?  
2. When does the object reach its maximum height? 
3. What is the object's maximum height? 
4. When does the object hit the ground?
5. Another object is launched from a different platform and the function that models the height as a function of time is $h(t)=-16t^2+80t+60$, is the maximum height of the second object higher or lower than the first? What is the maximum height?

You shoot a basketball from a height of 6 feet. The ball leaves your hands with a velocity of 32 ft/second. The equation of the function that models the height as a function of time is $h(t)=-16t^2+32t+6$

1. What is the maximum height your ball reaches? 
2. If the basketball hoop is 10 feet tall, how long does it take your ball to reach the hoop?

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

IMAGES CREATED BY GAVS