Basketball!!

The Basketball Parabola

Kobe Bryant passes the ball to his team mate during the second game of the season. He throws it up and away to make it across the court without an interference. It goes up 7 ft in the air and gets 22 ft across the court to his team mate, Steve Nash. What is the equation of this parabola??

The Equation

Real World Example # 1

The Equation

1. I find the vertex which is (10,5).

2. Next, I plug in the point (0,0) which is where the server hit the ball from, into the equation.

3. I solve the equation:

y=a(x-h)^2+k

0=a(0-10)^2+5

0=a(-10)^2+5

-5=100a

a=-.05

Therefore, the overall equation is

y=-.05(x-10)^2+5

Find at least three real world examples of parabolas in art, architecture, engineering, sports, or nature. Take pictures and actual measurements (as able).

a. Create equations that model the parabolas you find.

b. Describe the purpose of studying parabolas, as related to the examples you use.

c. How will transforming your parabolas impact their use(s) and/or effectiveness.

d. Explain your choice in parabolas studied (personal interest in topic?) and how this learning experience may impact future studies or pursuits.

e. Create three well-worded questions that can be answered with your model. Include a question that requires a transformation of your model and the impact of the transformation.

**Real Life Examples of Parabolas**

In volleyball, after an underhand serve, the ball goes up over the net reaching it's maximum point, and then slopes downwards back at the ground. This is a parabola. If the server hits the ball from directly behind the net (0,0), the net is 10ft high, and the ball goes 10 ft across the court, then what is the equation??

Graph...

Please refer to written work, pg 1, problem 1 for graph.

Thank you!

In order to complete and solve the equation, I graphed it first, to help me see what I was working with. Here is my process for calculating the "a" term, and then finding the entire equation.

1. I found the vertex, which is (7,11).

2. I plugged in the x and y values from any points on the graph. I used (0,0).

3. Now that the variables were all filled in (excluding "a") I could solve the equation.

1. 0=a(0-7)^2+11

2. 0=a(49)+11

3. -11=a(49)

4. a=-.224

Therefore, the equation is

y=-.224(x-7)^2+11

Graph...

Real Life Example #3

The Equation

To solve this problem, just like the others, I plug in the values and then solve.

1. I located the vertex which is (1.5,4.5).

2. I plugged in the h, k, x, and y values into the equation.

1. y=a(x-h)^2+k

2. 0=a(0-1.5)^2+4.5

3. 0=a(2.25)+4.5

4. -4.5=2.25a

5. a=-2

6. Therefore, the equation is y=-2(x-1.5)^2=4.5

When the diver jumps off the

board, she jumps up 4.5ft and

then dives down into the water.

Her total distance is 3ft out. What

is the equation?

Graph 2 & Work

Graph 1 & Work

Graph 3

Why Is Studying Parabolas important?

Studying parabolas is very important

because