# Investigating general parabola (AASL 2.6)

## Keywords

Parabola | 放物線 | 포물선 | 抛物线 |

Standard Form | 標準形式 | 표준형 | 标准形式 |

Vertex | 頂点 | 정점 | 顶点 |

Direction of Parabola | 放物線の方向 | 포물선의 방향 | 抛物线的方向 |

Axis of Symmetry | 対称軸 | 대칭축 | 对称轴 |

Coefficient | 係数 | 계수 | 系数 |

Completing the Square | 平方完成 | 완전제곱식으로 변환 | 配方法补全平方 |

Vertex Form | 頂点形式 | 정점 형태 | 顶点形式 |

Discriminant | 判別式 | 판별식 | 判别式 |

Quadratic Equation | 二次方程式 | 이차방정식 | 二次方程 |

Factual Questions | Conceptual Questions | Debatable Questions |

1. What is the standard form of a parabola? | 1. Why does a parabola open upwards when the coefficient of is positive? | 1. Is the vertex form more useful than the standard form for graphing parabolas? Why or why not? |

2. How do you find the vertex of a parabola given its equation in standard form? | 2. Explain the relationship between the focus, directrix, and vertex of a parabola. | 2. Can parabolas represent real-world situations more effectively than linear functions? |

3. What determines the direction (upwards or downwards) of a parabola? | 3. Discuss how the concept of completing the square is used to convert a quadratic equation to vertex form. | 3. Debate the importance of understanding the concept of the focus and directrix in the study of parabolas. |

4. How do you find the axis of symmetry for the parabola ? | 4. How does changing the value of 'a' in the equation affect the shape of the parabola? | 4. Discuss the statement: "The properties of parabolas are inherently more complex than those of circles." |

5. Compare and contrast the graphs of two parabolas with the same vertex but different orientations. | 5. Evaluate the impact of digital graphing tools on students' understanding of the properties of parabolas. |

1. Parabolic Patterns: Notice the equation What happens if you change the value of 'a' value? How does the parabola change?

2. The Discriminant Discovery: The discriminant in our quadratic formula is . Play around with different '', '', and '' values. Can you find a set of values where the discriminant is zero? What does this tell you about the graph?

## The b^2-4ac is called the discriminant. In the applet above you may have discovered what it tell us about the number of solutions.

3. Axis of Symmetry: The vertical pink line is called the axis of symmetry. If we change '', ' and '' which parameters affects the axes of symmetry? How can the axes of symmetry be calculated?

## Key features of quadratics summary

## IB-Specific and use of TI-calculator

## Extension

4. Vertex Venture: As you change the '' value. How does the vertex move? Can you work out the path of the vertex in terms of ?

## Extension

5.Vertex Venture: As you change the '' value. How does the vertex move? Can you work out the path of the vertex in terms of ?