Analyze Functions using different representations
F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Essential Question:
How tall must the gym be to make a full court shot?
Have you ever noticed how tall a basketball gym is compared to a volleyball gym? Why are they different? What about an indoor football arena? Do they just make up random heights that have no rhyme or reason?
This lesson is all about the investigation of what it would take to build a gymnasium that is tall enough to host a basketball game worthy of seeing a results like the video above. Nothing could be worse than seeing this video end with the ball clanking off of the roof because it wasn't tall enough!
This lesson is all about the investigation of what it would take to build a gymnasium that is tall enough to host a basketball game worthy of seeing a results like the video above. Nothing could be worse than seeing this video end with the ball clanking off of the roof because it wasn't tall enough!
Warm-up activity
- Sketch out the shot that just happened. Below are the dimensions of a basketball court. Use as much detail as possible in your sketch.
- Include the flight path that you think the basketball took from the time it left the athlete's hand until it hit the netting at the opposite end of the court
- How far do you think the ball traveled, based only on the video that you saw?
Completing Your Graph
Now that you have sketched the path of the basketball's flight, let's put some of the math into work. Include the following elements into your sketch as a way to reinforce what we have discussed in previous lessons:
Here's what you have found:
- Overlay a coordinate grid onto your sketch
- Identify the Axis of Symmetry (AoS)
- Identify the Vertex
- Identify the Zeroes (or Roots) of the function
Here's what you have found:
- the Axis of the Symmetry is the point in which the basketball's trajectory goes from moving upward to moving downward, letting you know that the height of the building is no longer relevant to keeping the ball in the gym
- The Vertex lets you know the point in the gym that must be the tallest, although most gyms are the same height across the entire ceiling
- The Zeroes of the function allow you to set the distance in which the ball will (more than likely) be shot the farthest while being aimed at the hoop
Finding A Possible Solution
Using Desmos and the background knowledge about quadratics, create a quadratic equation that represents the flight of the basketball. Manipulate the equation until the parabola matches the sketch that you have created. For a possible solution, click HERE.
Individual PracticeClick HERE for the individual practice with graphing quadratic functions.
Addition help for graphing quadratics |
Additional Practice (HW)Find 5 places in every day life where you see parabolic curves (quadratic functions). Sketch each scenario out onto a sheet of graph paper. Identify all parts of the graph, like in the warm-up, and determine the equation of the parabola using Desmos.
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