- Parabolas
- Constructing Graphs of Parabolas

Inside Collection (Textbook): Elementary Algebra

Summary: This module is from Elementary Algebra</link> by Denny Burzynski and Wade Ellis, Jr. Methods of solving quadratic equations as well as the logic underlying each method are discussed. Factoring, extraction of roots, completing the square, and the quadratic formula are carefully developed. The zero-factor property of real numbers is reintroduced. The chapter also includes graphs of quadratic equations based on the standard parabola, y = x^2, and applied problems from the areas of manufacturing, population, physics, geometry, mathematics (numbers and volumes), and astronomy, which are solved using the five-step method. Objectives of this module: be able to construct the graph of a parabola.

- Parabolas
- Constructing Graphs of Parabolas

We will now study the graphs of quadratic equations in two variables with general form

All such graphs have a similar shape. The graph of a quadratic equation of this type Parabola is called a *parabola* and it will assume one of the following shapes.

The high point or low point of a parabola is called the *vertex* of the parabola.

We will construct the graph of a parabola by choosing several

Graph

0 | 0 |

1 | 1 |

2 | 4 |

3 | 9 |

1 | |

4 | |

9 |

This is the most basic parabola. Although other parabolas may be wider, narrower, moved up or down, moved to the left or right, or inverted, they will all have this same basic shape. We will need to plot as many ordered pairs as necessary to ensure this basic shape.

Graph

0 | |

1 | |

2 | 2 |

3 | 7 |

2 | |

7 |

Notice that the graph of

Use the idea suggested in Sample Set A to sketch (quickly and perhaps not perfectly accurately) the graphs of

Graph

Do we expect the graph to be similar to the graph of

0 | 4 |

1 | 9 |

1 | |

0 | |

1 | |

4 |

Notice that the graph of

Use the idea suggested in Sample Set B to sketch the graphs of

Graph

For the following problems, graph the quadratic equations.

For the following problems, try to guess the quadratic equation that corresponds to the given graph.

*((Reference))* Simplify and write

*((Reference))* Factor

*((Reference))* Find the sum:

*((Reference))* Simplify

*((Reference))* Four is added to an integer and that sum is doubled. When this result is multiplied by the original integer, the product is

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Comments:"Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"