For this discussion you will need tape, a ruler or yardstick, and a small object that will not bounce, such as a bottle cap or an eraser. Mark a spot at the bottom of a wall with a small piece of tape. Starting at this piece of tape, throw the small object up and forward so that it travels in an arc and brushes the wall. Use your other hand to quickly mark the spot on the wall where the object reached the top of the arc. Put a small piece of tape at this spot. Put a third piece of tape at the bottom of the wall where the object came to rest. Let the tape at the starting point be the origin. Use the ruler or yardstick to measure the horizontal and vertical distances from the origin to the tape at the top of the arc. Record the coordinates. Use the ruler or yardstick to measure the horizontal distance from the origin to the final resting point. Record the coordinates. You now have three pairs of coordinates from the path of the object. Describe your experience tossing the object and finding the three pairs of coordinates. List the three pairs of coordinates. Then use the coordinates to write the equation of a quadratic function that models the data. Show your work and comment on any challenges that you had

Question

For this discussion you will need tape, a ruler or yardstick, and a small object that will not bounce, such as a bottle cap or an eraser. Mark a spot at the bottom of a wall with a small piece of tape. Starting at this piece of tape, throw the small object up and forward so that it travels in an arc and brushes the wall. Use your other hand to quickly mark the spot on the wall where the object reached the top of the arc. Put a small piece of tape at this spot. Put a third piece of tape at the bottom of the wall where the object came to rest. Let the tape at the starting point be the origin. Use the ruler or yardstick to measure the horizontal and vertical distances from the origin to the tape at the top of the arc. Record the coordinates. Use the ruler or yardstick to measure the horizontal distance from the origin to the final resting point. Record the coordinates. You now have three pairs of coordinates from the path of the object. Describe your experience tossing the object and finding the three pairs of coordinates. List the three pairs of coordinates. Then use the coordinates to write the equation of a quadratic function that models the data. Show your work and comment on any challenges that you had

Use this as an example of how to write your answer.
"For the coordinates, I got (0,0) (4,8) (8,0). Using the general form of y=ax^2 +bx + c, we can substitute the numbers in "

Answer 1

For my experience tossing the object and finding the three pairs of coordinates, I found it to be quite straightforward. I marked the starting point with a small piece of tape and then threw the object in an arc so that it brushed the wall. Using my other hand, I quickly marked the spot on the wall where the object reached the top of the arc and put a small piece of tape there. I then marked the final resting point of the object on the wall with a third piece of tape.

The three pairs of coordinates I obtained from this are:

Starting point: (0,0)
Top of the arc: (x1,y1)
Final resting point: (x2,y2)

Using the ruler or yardstick, I measured the horizontal and vertical distances from the starting point to the tape at the top of the arc, and recorded the respective coordinates.

Now, to find the equation of the quadratic function that models the data, we can use the general form: y = ax^2 + bx + c.

Using the coordinates (0,0) for the starting point, we can see that c = 0.

To find the values of a and b, we can substitute the coordinates (x1,y1) and (x2,y2) into the equation.

Substituting (x1,y1) = (4,8) into the equation, we get:
y1 = a(4^2) + b(4) + 0
8 = 16a + 4b

Substituting (x2,y2) = (8,0) into the equation, we get:
y2 = a(8^2) + b(8) + 0
0 = 64a + 8b

We now have a system of two equations with two variables:
16a + 4b = 8
64a + 8b = 0

Solving this system, we can find the values of a and b.
Dividing the first equation by 4, we get:
4a + b = 2

Now, subtracting this equation from the second equation, we eliminate b:
64a + 8b - (4a + b) = 0 - 2
60a + 7b = -2

Solving these equations simultaneously, we find:
a ≈ -0.049
b ≈ 0.307

Therefore, the equation of the quadratic function that models the data is:
y = -0.049x^2 + 0.307x + 0

One challenge I encountered during this process was accurately marking the spot on the wall where the object reached the top of the arc. Since the object was moving in a fast motion, it was difficult to precisely mark the exact point. However, I tried my best to estimate it as accurately as possible.