Bball Parabola Handout

Parabolas in Real Life 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 We are going to be modeling the parabola above using a quadratic model. Question: What again is a model?

To start, we need to write down a number of points that are on the parabola. I want you to choose points that are neither xintercepts nor at the vertex (or turning-point) of the parabola, because we will be using the model to estimate these points. To get a good model, you will need pick points from both sides of the parabola (left and right). Pick any seven points and enter their x- and y-coordinates in the chart to the right.

x

y

1. Now, please go back and use your calculator reference sheet to find a quadratic model. Graph it to make sure it is a good model, and then write the equation down here:

2. What are a, b, and c in the equation above?

3. Now, please flip back to the front side and estimate the coordinates of the vertex (or turning point) at which the parabola reaches its maximum. Write it here:

4. What is

−b ? 2a

5. Do you see any relationship between the answers in question numbers 3 and 4?

6. Now, take the answer from question number 4 and plug it into your equation that you wrote down in question number 1. −b Another way to think about this: What is y when x is equal to ? 2a

7. Do you see any relationship between the answers in questions 3 and 6?

8. In your own words, how would you find the turning point in a quadratic?