Administration



Example1:

Amery recorded the distance and height of

a basketball when shooting a free throw.

1. Find the quadratic equation for the

relationship of the horizontal distance

and the height of the ball.

2. Using this function what is the approximate

maximum height of the ball?

[pic]

Example 2. The pizza prices at a pizza parlor are $9.95 for a 12 inch, $13.95 for a 14 inch, and $16.95 for a 16 inch pizza.

a. Find a quadratic model for the price of a pizza based on the size (diameter).

b. Use the model to find the price of an 18 inch pizza.

c. Is the quadratic function a good model for the price of a pizza? Explain your reasoning.

Practice

1) This table shows the population of a city

every ten years since 1970.

a. Find the best-fitting quadratic model

for the data.

b. Using this model, what will be the

estimated population in 2020?

2) The data table shows the energy, E, of a certain object in joules at a given velocity, v, in meters per second.

|Energy ( joules) |4.5 |12.5 |24.5 |40.5 |

|Velocity (m/s) |1.5 |2.5 |3.5 |4.5 |

a.) Find the quadratic equation for the relationship between the energy and the velocity of the object.

b) what is the velocity of the object if the energy is 128 joules?

3) Use the table below to answer the questions about the operating costs in thousands of a small business from 2000 to 2007.

Year, t2000 (0)2001(1)2002 (2)2003 (3)2004 (4)2005 (5)2006 (6)2007 (7)Operating Costs2.32.63.13.34.05.25.97.0

a) Find the best fitting quadratic model for this data.

b) Using this model, what will be the operating costs in 2010?

Practice

[pic]

1. Which of the following is best modeled by a quadratic function?

Relationship between circumference and diameter.

Relationship between area of a square and side length.

Relationship between diagonal of a square and side length.

Relationship between volume of a cube and side length.

[pic]

2. If y is a quadratic function of x, which value completes the table?

12

20

44

48

[pic]

The graph of a quadratic function having the form f(x) = ax2 + bx + c passes through the points (0, -8), (3, 10), and (6, 34). What is the value of the function when x = -3?

-32

-26

-20

10

[pic]

Which is the quadratic equation the best fits the scatterplot?

a. [pic] a. [pic]

b. [pic] b. [pic]

c. [pic] c. [pic]

d. [pic] d. [pic]

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|Vocabulary: |Height (feet), |

|Regression: the mathematical|f(x) |

|process for determining an | |

|equation from a set of given| |

|data | |

|Quadratic Regression: the | |

|process of finding the | |

|equation of a parabola that | |

|fits a given set of data. | |

| | |

|Calculator Steps: ( make | |

|sure to clear the memory on | |

|your calculator – Press | |

|clear & on at the same time)| |

|1. Hit Data-enter x-values | |

|into L1 and y-values into L2| |

|2. Hit 2nd mode (quit) | |

|3. Hit 2nd data | |

|(stat-reg/distr) , tab down | |

|to #5 ( Quadratic Reg) and | |

|enter. | |

|4. Enter until calc is | |

|highlighted then enter (give| |

|the calculator a few seconds| |

|to process the information | |

|5. Write the values of a, b,| |

|and c (Round to 3 decimal | |

|place) | |

|6. Substitute the values | |

|into [pic] | |

| | |

| | |

| | |

| | |

|Distance(feet), | |

|x | |

|0 |4 |

|2 |8.4 |

|6 |12.1 |

|9 |14.2 |

|12 |13.2 |

|13 |10.5 |

|15 |9.8 |

|Years Since 1970, |Population |

|x |(In thousands), y |

|0 |489 |

|10 |801 |

|20 |1,202 |

|30 |1,998 |

|40 |2,959 |

x |-2 |0 |2 |4 |6 | |y |-8 |0 |12 |28 | | |

6.

5

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