# Lesson 5

Building Quadratic Functions to Describe Situations (Part 1)

- Let’s measure falling objects.

### Problem 1

A rocket is launched in the air and its height, in feet, is modeled by the function \(h\). Here is a graph representing \(h\).

Select **all** true statements about the situation.

The rocket is launched from a height less than 20 feet above the ground.

The rocket is launched from about 20 feet above the ground.

The rocket reaches its maximum height after about 3 seconds.

The rocket reaches its maximum height after about 160 seconds.

The maximum height of the rocket is about 160 feet.

### Problem 2

A baseball travels \(d\) meters \(t\) seconds after being dropped from the top of a building. The distance traveled by the baseball can be modeled by the equation \(d = 5t^2\).

- Complete the table and plot the data on the coordinate plane.
\(t\) (seconds) \(d\) (meters) 0 0.5 1 1.5 2 - Is the baseball traveling at a constant speed? Explain how you know.

### Problem 3

A rock is dropped from a bridge over a river. Which table could represent the distance in feet fallen as a function of time in seconds?

Table A

time (seconds) | distance fallen (feet) |
---|---|

0 | 0 |

1 | 48 |

2 | 96 |

3 | 144 |

Table B

time (seconds) | distance fallen (feet) |
---|---|

0 | 0 |

1 | 16 |

2 | 64 |

3 | 144 |

Table C

time (seconds) | distance fallen (feet) |
---|---|

0 | 180 |

1 | 132 |

2 | 84 |

3 | 36 |

Table D

time (seconds) | distance fallen (feet) |
---|---|

0 | 180 |

1 | 164 |

2 | 116 |

3 | 36 |

Table A

Table B

Table C

Table D

### Problem 4

Determine whether \(5n^2\) or \(3^n\) will have the greater value when:

- \(n=1\)
- \(n=3\)
- \(n=5\)

### Problem 5

Select **all **of the expressions that give the number of small squares in Step \(n\).

\(2n\)

\(n^2\)

\(n+1\)

\(n^2+1\)

\(n(n+1)\)

\(n^2+n\)

\(n+n+1\)

### Problem 6

A small ball is dropped from a tall building. Which equation could represent the ball’s height, \(h\), in feet, relative to the ground, as a function of time, \(t\), in seconds?

\(h=100-16t\)

\(h=100-16t^2\)

\(h=100-16^t\)

\(h=100-\frac{16}{t}\)

### Problem 7

Use the rule for function \(f\) to draw its graph.

\(f(x)=\begin{cases} 2,& \text- 5\leq x< \text- 2 \\ 6,& \text- 2\leq x<4 \\ x, & 4\leq x<8\\ \end{cases}\)

### Problem 8

Diego claimed that \(10+x^2\) is always greater than \(2^x\) and used this table as evidence.

Do you agree with Diego?

\(x\) | \(10+x^2\) | \(2^x\) |
---|---|---|

1 | 11 | 2 |

2 | 14 | 4 |

3 | 19 | 8 |

4 | 26 | 16 |

### Problem 9

The table shows the height, in centimeters, of the water in a swimming pool at different times since the pool started to be filled.

- Does the height of the water increase by the same amount each minute? Explain how you know.
- Does the height of the water increase by the same factor each minute? Explain how you know.

minutes | height |
---|---|

0 | 150 |

1 | 150.5 |

2 | 151 |

3 | 151.5 |