When finding the following heights remember that the vertex is the highest or lowest point of the graph.
Problem #1
Nick jumps of a chair that is 12 inches high. He has his cool new Buzz Lightyear Wings and wants to try flying. The quadratic that represents the equation of him jumping after x seconds is y=-x2+4x+12. The value of y determines his height after x seconds. What is his highest height Nick achieved? How many seconds did it take him to reach his highest height?
Problem #2
Beatrice is the star player of her soccer team. She’s known for kicking the ball high enough where it is impossible for the goalie to stop the ball from getting in. In the following video, the quadratic function that represents the height of the ball in yards after x seconds is y=-x2+3.75x+3. The value of y determines the height of the ball after x seconds. What is the highest height of that ball?
Problem #3
The equation y=-16x2+35x models the height of the ball after Chuck kicks it. The height is represented by y and the seconds is represented by x. What is the highest height the football reached after Chuck kicked it?
Problem #4
Maurice the Bear loves to skateboard. Maurice decides to go skateboarding on a platform that is 9 ft high. The equation y=0.25x2-3x+9 represents the height (y) after x seconds. After how many seconds does Maurice reach the bottom of the platform (lowest point)?
Now it is your turn to create your own real world application of a quadratic equation. Pick one equation from the list below. Graph the equation. Then create a story and draw a picture that goes along with it. You may draw your picture on your graph. Upload your assignment on Google Docs and publish the link in the Blog area. If you have an idea but need help developing it, leave a message in the Blog area as well.
1. y = 2x2-4x+4
2. y = -2x2-4x+2
3. y = 2x2+16x+35
4. y = -x2-2x+1
5. y = 2x2-4x+4
6. y = 3x2-24x+46
Click on the graph below if you are in need of graph paper.
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